Topological And Symbolic Dynamics
DOWNLOAD
Download Topological And Symbolic Dynamics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topological And Symbolic Dynamics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Topological And Symbolic Dynamics
DOWNLOAD
Author : Petr Kůrka
language : en
Publisher: Société Mathématique de France
Release Date : 2003
Topological And Symbolic Dynamics written by Petr Kůrka and has been published by Société Mathématique de France this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Symbolic dynamics categories.
A dynamical system is a continuous self-map of a compact metric space. Topological dynamics studies the iterations of such a map, or equivalently, the trajectories of points of the state space. The basic concepts of topological dynamics are minimality, transitivity, recurrence, shadowing property, stability, equicontinuity, sensitivity, attractors, and topological entropy. Symbolic dynamics studies dynamical systems whose state spaces are zero-dimensional and consist of sequences of symbols. The main classes of symbolic dynamical systems are adding machines, subshifts of finite type, sofic subshifts, Sturmian, substitutive and Toeplitz subshifts, and cellular automata.
Symbolic Dynamics And Its Applications
DOWNLOAD
Author : Peter Walters
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Symbolic Dynamics And Its Applications written by Peter Walters and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honour of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including: ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.
Symbolic Dynamics
DOWNLOAD
Author : Bruce P. Kitchens
language : en
Publisher: Springer
Release Date :
Symbolic Dynamics written by Bruce P. Kitchens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.
Symbolic Dynamics
DOWNLOAD
Author : Bruce P. Kitchens
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symbolic Dynamics written by Bruce P. Kitchens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.
Symbolic Dynamics And Its Applications
DOWNLOAD
Author : Susan G. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Symbolic Dynamics And Its Applications written by Susan G. Williams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.
Groups And Topological Dynamics
DOWNLOAD
Author : Volodymyr Nekrashevych
language : en
Publisher:
Release Date : 2022
Groups And Topological Dynamics written by Volodymyr Nekrashevych and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Finite groups categories.
This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of.
Applied Symbolic Dynamics And Chaos
DOWNLOAD
Author : Bailin Hao
language : en
Publisher: World Scientific
Release Date : 1998-07-04
Applied Symbolic Dynamics And Chaos written by Bailin Hao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-04 with Science categories.
Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.
Topological And Ergodic Theory Of Symbolic Dynamics
DOWNLOAD
Author : Henk Bruin
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-21
Topological And Ergodic Theory Of Symbolic Dynamics written by Henk Bruin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-21 with Mathematics categories.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.
Applied Symbolic Dynamics And Chaos Second Edition
DOWNLOAD
Author : Hao Bailin
language : en
Publisher: World Scientific
Release Date : 2018-05-11
Applied Symbolic Dynamics And Chaos Second Edition written by Hao Bailin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-11 with Science categories.
Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps
DOWNLOAD
Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.