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| devil's staircase math: Imagine Math 6 Michele Emmer, Marco Abate, 2018-11-06 Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine combining music, art, poetry, literature, architecture and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics. This sixth volume in the series begins with a homage to the architect Zaha Hadid, who died on March 31st, 2016, a few weeks before the opening of a large exhibition of her works in Palazzo Franchetti in Venice, where all the Mathematics and Culture conferences have taken place in the last years. A large section of the book is dedicated to literature, narrative and mathematics including a contribution from Simon Singh. It discusses the role of media in mathematics, including museums of science, journals and movies. Mathematics and applications, including blood circulation and preventing crimes using earthquakes, is also addressed, while a section on mathematics and art examines the role of math in design. A large selection presents photos of mathematicians and mathematical objects by Vincent Moncorge. Discussing all topics in a way that is rigorous but captivating, detailed but full of evocations, it offers an all-embracing look at the world of mathematics and culture. |
| devil's staircase math: Geometry In Advanced Pure Mathematics Shaun Bullett, Tom Fearn, Frank Smith, 2017-03-07 This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces.Geometry in Advanced Pure Mathematics is the fourth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas. |
| devil's staircase math: Fractals, Graphics, and Mathematics Education Michael Frame, Benoit Mandelbrot, 2002-06-20 Publisher Description |
| devil's staircase math: Mathematical Constants Steven R. Finch, 2003-08-18 Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place. |
| devil's staircase math: Hamiltonian Dynamical Systems R.S MacKay, J.D Meiss, 2020-08-18 Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics. |
| devil's staircase math: Geometry of Riemann Surfaces William J. Harvey, Frederick P. Gardiner, Gabino González-Diez, Christos Kourouniotis, 2010-02-11 Original research and expert surveys on Riemann surfaces. |
| devil's staircase math: Rotation Sets and Complex Dynamics Saeed Zakeri, 2018-06-23 This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields. |
| devil's staircase math: Complex Dynamics Dierk Schleicher, 2009-11-03 Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published |
| devil's staircase math: Dynamics & Stochastics Michael S. Keane, Dee Denteneer, Frank Hollander, Evgeny Verbitskiy, 2006 |
| devil's staircase math: Mathematical Results In Statistical Mechanics Jean Ruiz, Salvador Miracle-sole, Valentin Zagrebnov, 1999-05-14 This invaluable book is a collection of lectures delivered at the Colloquium 'Mathematical Results in Statistical Mechanics' held in Marseilles, France, on July 27-31, 1998, as a satellite colloquium of the Paris conference STATPHYS 20. It covers a large part of the contemporary results in statistical mechanics, from the point of view of mathematical physics, by leading experts in this field. It includes as the main topics, phase transitions, interfaces, disordered systems, Gibbsian and non-Gibbsian states, as well as recent rigorous treatments in quantum statistical mechanics. |
| devil's staircase math: Introduction to the Modern Theory of Dynamical Systems Anatole Katok, A. B. Katok, Boris Hasselblatt, 1995 This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. |
| devil's staircase math: Mathematics Unlimited - 2001 and Beyond Björn Engquist, Wilfried Schmid, 2017-04-05 This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a must-read for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only. |
| devil's staircase math: New Trends in One-Dimensional Dynamics Maria José Pacifico, Pablo Guarino, 2019-12-14 This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016. Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo’s co-authors and former doctoral students. Sadly, Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field. |
| devil's staircase math: Mathematical Aspects of Classical and Celestial Mechanics Vladimir I. Arnold, Valery V. Kozlov, Anatoly I. Neishtadt, 2007-07-05 The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory. |
| devil's staircase math: The Devil's Staircase Helen Fitzgerald, 2012-12-17 Bronny, a young Australian, finds herself down and out in London. She's a sweet girl who has spent her teenage years in a fearful, cautious bubble. She's never taken drugs, had sex or killed anyone. Within six weeks she's done all three. A group of backpackers break into an abandoned London townhouse seeking a rent-free life of debauchery. They don't realise someone's already there: a terrified woman bound and gagged in the basement. The Devil's Staircase combines a chick-lit voice and a dark crime noir environment. Not for the faint-hearted, The Devil's Staircase is funny, sexy and disturbing - it will keep you on the edge of your seat from start to finish. |
| devil's staircase math: Mathematical Aspects of Classical and Celestial Mechanics V.I. Arnold, Victor V. Kozlov, A.I. Neishtadt, 2013-12-01 From the reviews: ... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ... American Mathematical Monthly, Nov. 1989 This is a book to curl up with in front of a fire on a cold winter's evening. ... SIAM Reviews, Sept. 1989 |
| devil's staircase math: CRC Concise Encyclopedia of Mathematics Eric W. Weisstein, 2002-12-12 Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
| devil's staircase math: Ergodic Dynamics Jane Hawkins, 2021-01-28 This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability. |
| devil's staircase math: Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena Mariana Montiel, Robert W Peck, 2018-11-08 Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. |
| devil's staircase math: Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot Michel Laurent Lapidus, Machiel Van Frankenhuysen, 2004 This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications. |
| devil's staircase math: Laminational Models for Some Spaces of Polynomials of Any Degree Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin, 2020-09-28 The so-called 'pinched disk' model of the Mandelbrot set is due to A. Douady, J. H. Hubbard, and W. P. Thurston. It can be described in the language of geodesic laminations. |
| devil's staircase math: Combinatorial Dynamics And Entropy In Dimension One (2nd Edition) Luis Alseda, Jaume Llibre, Michal Misiurewicz, 2000-10-31 This book introduces the reader to the two main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all cycles (periodic orbits) of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.; it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of “chaos” present in it; for that the topological entropy is used. The book analyzes the combinatorial dynamics and topological entropy for the continuous maps of either an interval or the circle into itself. |
| devil's staircase math: Introduction to Discrete Dynamical Systems and Chaos Mario Martelli, 2011-11-01 A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field. |
| devil's staircase math: On Musical Self-similarity Gabriel Pareyón, 2011 |
| devil's staircase math: A Random Walk Through Fractal Dimensions Brian H. Kaye, 2008-07-11 Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: ...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems. MRS Bulletin |
| devil's staircase math: Extremes and Recurrence in Dynamical Systems Valerio Lucarini, Davide Faranda, Ana Cristina Gomes Monteiro Moreira de Freitas, Jorge Miguel Milhazes de Freitas, Mark Holland, Tobias Kuna, Matthew Nicol, Mike Todd, Sandro Vaienti, 2016-03-28 Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France. |
| devil's staircase math: Lectures on the Philosophy of Mathematics Joel David Hamkins, 2021-03-09 An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations. |
| devil's staircase math: Mathematical Reviews , 2006 |
| devil's staircase math: Fractals for the Classroom Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2012-12-06 Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many fascinating insights for the classroom teacher and integrates illustrations from a wide variety of applications with an enjoyable text to help bring the concepts alive and make them understandable to the average reader. This book will have a tremendous impact upon teachers, students, and the mathematics education of the general public. With the forthcoming companion materials, including four books on strategic classroom activities and lessons with interactive computer software, this package will be unparalleled. |
| devil's staircase math: Chaos and Fractals Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, 2013-06-29 For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals. |
| devil's staircase math: Singularity Theory and Equivariant Symplectic Maps Thomas J. Bridges, Jacques E. Furter, 2006-11-15 The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory. |
| devil's staircase math: Combinatorics, Words and Symbolic Dynamics Valérie Berthé, Michel Rigo, 2016-02-26 Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms. |
| devil's staircase math: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Kenneth Meyer, Glen Hall, 2013-04-17 The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given. |
| devil's staircase math: Glimpses into the World of Mathematics LIT Verlag, 2021-01-01 Essays collected in this volume deal with various problems from the philosophy of mathematics. What connects them are two questions: how mathematics is created and how it is acquired. In 'Three Worlds of Mathematics' we are familiarized with David Tall's ideas pertaining to the embodied, symbolic and formal worlds of mathematics. In 'Basic Ideas of Intuitionism', we focus on an epistemological approach to mathematics which is distinctive to constructive mathematics. The author focuses on the computational content of intuitionistic logic and shows how it relates to functional programming. 'The Brave Mathematical Ant' carefully selects mathematical puzzles related to teaching experiences in a way that the solution requires creativity and is not obtainable by following an algorithm. Moreover the solution gives us some new insight into the underlying idea. 'Degrees Of Accessibility Of Mathematical Objects' discusses various criteria which can be used to judge accessibility of mathematical objects. We find logical complexity, range of applications, existence of a physical model as well as aesthetic values. Jerzy Pogonowski, Faculty of Psychology and Cognitive Sciences, Adam Mickiewicz University, Pozna? Szymon Chlebowski, Faculty of Psychology and Cognitive Sciences, Adam Mickiewicz University, Pozna? Barbara Borkowicz, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Pozna? |
| devil's staircase math: Capture Dynamics and Chaotic Motions in Celestial Mechanics Edward Belbruno, 2018-06-05 This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering. |
| devil's staircase math: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields John Guckenheimer, Philip Holmes, 2013-11-21 An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved. |
| devil's staircase math: Toward a Science Campus in Milan Pier Francesco Bortignon, Giuseppe Lodato, Emanuela Meroni, Matteo G.A. Paris, Laura Perini, Alessandro Vicini, 2018-12-08 This book is a collection of multidisciplinary papers presented at the Department of Physics of Milan University's congress on 28 and 29 June 2017, which was also intended as a kick-off meeting for the design of a novel science campus at the Expo site in Milan. The congress presented a snapshot of the department's research to the academic community, the media, policymakers and authorities as well as the public at large, and also provided an opportunity to strengthen interdisciplinary collaborations between the members of the department and other communities. This book is a valuable resource for scientists looking for synergetic projects, policymakers wanting to grasp scientists' points of view and for prospective graduate students seeking expanding areas of research. |
| devil's staircase math: Topics in Ergodic Theory (PMS-44), Volume 44 Iakov Grigorevich Sinai, 2017-03-14 This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. |
| devil's staircase math: Differentiation of Real Functions A. M. Bruckner, 2006-11-15 |
| devil's staircase math: Introduction to Applied Nonlinear Dynamical Systems and Chaos Stephen Wiggins, 2006-04-18 This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: Will serve as one of the most eminent introductions to the geometric theory of dynamical systems. --Monatshefte für Mathematik |
Devil 和 Demon 的区别是什么？ - 知乎
Devil is the ultimate evil spirit or the god of evil. Demons are spirits that do the work of the devil. However, sometimes they are used interchangeably. Another popular way to use "devil": As …
demon和devil有什么区别？ - 知乎
相对于demon，devil是比较高级的恶魔。 Devil: 一般来说，devil是恶魔头头，能叫devil的恶魔，层次都非常高，都是Satan、Lucifer之类的魔鬼。此外，devil有强烈的宗教意味，基本上都用来 …
请问恶魔（英语里应该是Demon）与魔鬼（英语中为Devil）在西方 …
devil相当于你看到的教父里的黑手党，除了devil不是家族结构，他们干坏事是为了利益，会提前计划好，不会随随便便搞事情（教父Ⅲ里的丹特因为拷问一个人时过于残忍而被批评过）。
英文中的devil和demon还有evil有什么区别？ - 知乎
但等级有些不同，可以这样记，devil是demon的首领。 再者“Demon”有时可形容一个人对某件事的投入，比如“he studied English every day for 10 hours like a demon” 而devil 有时会会用做对 …
有问题，就会有答案 - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
路西法（Lucifer）和撒旦是什么关系？ - 知乎
但是，有一点值得我们注意。当时还存在着一种次要传统，将路西法和撒但区别开来，只有路西法才是完全对立于上帝的魔鬼（the devil）。比如，在我们提到的威廉 ? 兰格伦的《农夫皮尔斯 …
2025年AMD显卡推荐哪个品牌好性价比高？（4500字选购攻略）
May 12, 2025 · 可额外购买通过磁吸固定的可替换背板Devil Skins，让显卡背板具备独特风格。 正面、侧边与背板的RGB能通过软件或连接信号线与其他设备同步，轻松打造专属灯效。 规 …
INTP T和 INTP A 的区别是什么？ - 知乎
intp-t内耗自闭 谨慎 心理创伤严重 . intp-a自信乐观 不容易内耗 . 都不擅长社交. intp-a 像infp+ entj intp-t像intj +entp
中级经济师难考吗？通过率高吗？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
游戏史上各个时期有哪些「里程碑」级别的游戏？ - 知乎
《鬼泣》/《Devil May Cry》 CAPCOM/PS2/2001 “3D动作游戏鼻祖” 三上真司对游戏品质的要求一直很高。 在生化危机成功后，1998年的生化危机2就曾经经历过一次全盘推倒重做（即坊间称 …
Devil 和 Demon 的区别是什么？ - 知乎
Devil is the ultimate evil spirit or the god of evil. Demons are spirits that do the work of the devil. However, sometimes they are used interchangeably. Another popular way to use "devil": As an …
demon和devil有什么区别？ - 知乎
相对于demon，devil是比较高级的恶魔。 Devil: 一般来说，devil是恶魔头头，能叫devil的恶魔，层次都非常高，都是Satan、Lucifer之类的魔鬼。此外，devil有强烈的宗教意味，基本上都用来 …
请问恶魔（英语里应该是Demon）与魔鬼（英语中为Devil）在西 …
devil相当于你看到的教父里的黑手党，除了devil不是家族结构，他们干坏事是为了利益，会提前计划好，不会随随便便搞事情（教父Ⅲ里的丹特因为拷问一个人时过于残忍而被批评过）。
英文中的devil和demon还有evil有什么区别？ - 知乎
但等级有些不同，可以这样记，devil是demon的首领。 再者“Demon”有时可形容一个人对某件事的投入，比如“he studied English every day for 10 hours like a demon” 而devil 有时会会用做对 …
有问题，就会有答案 - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
路西法（Lucifer）和撒旦是什么关系？ - 知乎
但是，有一点值得我们注意。当时还存在着一种次要传统，将路西法和撒但区别开来，只有路西法才是完全对立于上帝的魔鬼（the devil）。比如，在我们提到的威廉 ? 兰格伦的《农夫皮尔斯 …
2025年AMD显卡推荐哪个品牌好性价比高？（4500字选购攻略）
May 12, 2025 · 可额外购买通过磁吸固定的可替换背板Devil Skins，让显卡背板具备独特风格。 正面、侧边与背板的RGB能通过软件或连接信号线与其他设备同步，轻松打造专属灯效。 规 …
INTP T和 INTP A 的区别是什么？ - 知乎
intp-t内耗自闭 谨慎 心理创伤严重 . intp-a自信乐观 不容易内耗 . 都不擅长社交. intp-a 像infp+ entj intp-t像intj +entp
中级经济师难考吗？通过率高吗？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
游戏史上各个时期有哪些「里程碑」级别的游戏？ - 知乎
《鬼泣》/《Devil May Cry》 CAPCOM/PS2/2001 “3D动作游戏鼻祖” 三上真司对游戏品质的要求一直很高。 在生化危机成功后，1998年的生化危机2就曾经经历过一次全盘推倒重做（即坊间称 …
