Topological Entropy And Equivalence Of Dynamical Systems

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Topological Entropy and Equivalence of Dynamical Systems

Author : Roy L. Adler
Publisher : American Mathematical Soc.
ISBN 13 : 0821822195
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topological Entropy and Equivalence of Dynamical Systems by : Roy L. Adler

Download or read book Topological Entropy and Equivalence of Dynamical Systems written by Roy L. Adler and published by American Mathematical Soc.. This book was released on 1979 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this work is to prove a theorem for topological entropy analogous to Ornstein's result for measure entropy. For this a natural class of dynamical systems is needed to play the same role for topological entropy as the Bernoulli shifts do for measure entropy. Fortunately there is just such a class--the topological Markov shifts. The main result of this paper is that topological entropy along with another number, called the ergodic period, is a complete set of invariants under this new equivalence relation for the class of topological Markov shifts.

Topological Entropy and Equivalence of Dynamical Systems

Author : American Mathematical Society
Publisher :
ISBN 13 : 9780821822180
Total Pages : 90 pages
Book Rating : 4.8/5 (221 download)

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Book Synopsis Topological Entropy and Equivalence of Dynamical Systems by : American Mathematical Society

Download or read book Topological Entropy and Equivalence of Dynamical Systems written by American Mathematical Society and published by . This book was released on 1979 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorial Dynamics And Entropy In Dimension One

Author : Alseda Luis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814553220
Total Pages : 344 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Combinatorial Dynamics And Entropy In Dimension One by : Alseda Luis

Download or read book Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis and published by World Scientific Publishing Company. This book was released on 1993-06-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy

Invariance Entropy for Deterministic Control Systems

Author : Christoph Kawan
Publisher : Springer
ISBN 13 : 3319012886
Total Pages : 290 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Invariance Entropy for Deterministic Control Systems by : Christoph Kawan

Download or read book Invariance Entropy for Deterministic Control Systems written by Christoph Kawan and published by Springer. This book was released on 2013-10-02 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.

Ergodic Theory and Topological Dynamics

Author :
Publisher : Academic Press
ISBN 13 : 0080873863
Total Pages : 201 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Ergodic Theory and Topological Dynamics by :

Download or read book Ergodic Theory and Topological Dynamics written by and published by Academic Press. This book was released on 1976-11-15 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic Theory and Topological Dynamics

Dynamical Systems, Graphs, and Algorithms

Author : George Osipenko
Publisher : Springer
ISBN 13 : 3540355952
Total Pages : 286 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Dynamical Systems, Graphs, and Algorithms by : George Osipenko

Download or read book Dynamical Systems, Graphs, and Algorithms written by George Osipenko and published by Springer. This book was released on 2006-10-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Dynamical Systems

Author : James C. Alexander
Publisher : Springer
ISBN 13 : 3540459464
Total Pages : 736 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamical Systems by : James C. Alexander

Download or read book Dynamical Systems written by James C. Alexander and published by Springer. This book was released on 2006-11-14 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume reflect the richness and diversity of the subject of dynamics. Some are lectures given at the three conferences (Ergodic Theory and Topological Dynamics, Symbolic Dynamics and Coding Theory and Smooth Dynamics, Dynamics and Applied Dynamics) held in Maryland between October 1986 and March 1987; some are work which was in progress during the Special Year, and some are work which was done because of questions and problems raised at the conferences. In addition, a paper of John Milnor and William Thurston, versions of which had been available as notes but not yet published, is included.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Algebraic and Topological Dynamics

Author : S. F. Koli︠a︡da
Publisher : American Mathematical Soc.
ISBN 13 : 0821837516
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Topological Dynamics by : S. F. Koli︠a︡da

Download or read book Algebraic and Topological Dynamics written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.

Global Theory of Dynamical Systems

Author : Z. Nitecki
Publisher : Springer
ISBN 13 : 3540383123
Total Pages : 508 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Global Theory of Dynamical Systems by : Z. Nitecki

Download or read book Global Theory of Dynamical Systems written by Z. Nitecki and published by Springer. This book was released on 2006-11-14 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Dynamical Systems and Applications

Author : Michael Brin
Publisher : Cambridge University Press
ISBN 13 : 9780521840736
Total Pages : 490 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Modern Dynamical Systems and Applications by : Michael Brin

Download or read book Modern Dynamical Systems and Applications written by Michael Brin and published by Cambridge University Press. This book was released on 2004-08-16 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.

Entropy in Dynamical Systems

Author : Tomasz Downarowicz
Publisher : Cambridge University Press
ISBN 13 : 1139500872
Total Pages : 405 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Entropy in Dynamical Systems by : Tomasz Downarowicz

Download or read book Entropy in Dynamical Systems written by Tomasz Downarowicz and published by Cambridge University Press. This book was released on 2011-05-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.

Local Entropy Theory of a Random Dynamical System

Author : Anthony H. Dooley
Publisher : American Mathematical Soc.
ISBN 13 : 1470410559
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local Entropy Theory of a Random Dynamical System by : Anthony H. Dooley

Download or read book Local Entropy Theory of a Random Dynamical System written by Anthony H. Dooley and published by American Mathematical Soc.. This book was released on 2014-12-20 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Handbook of Dynamical Systems

Author : B. Hasselblatt
Publisher : Elsevier
ISBN 13 : 0080533442
Total Pages : 1231 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Hasselblatt

Download or read book Handbook of Dynamical Systems written by B. Hasselblatt and published by Elsevier. This book was released on 2002-08-20 with total page 1231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

A Modern Introduction to Dynamical Systems

Author : Richard J. Brown
Publisher : Oxford University Press
ISBN 13 : 0191061018
Total Pages : 399 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis A Modern Introduction to Dynamical Systems by : Richard J. Brown

Download or read book A Modern Introduction to Dynamical Systems written by Richard J. Brown and published by Oxford University Press. This book was released on 2018-06-21 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics. Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.

Dynamical Systems

Author : Werner Krabs
Publisher : Springer Science & Business Media
ISBN 13 : 3642137229
Total Pages : 245 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Dynamical Systems by : Werner Krabs

Download or read book Dynamical Systems written by Werner Krabs and published by Springer Science & Business Media. This book was released on 2010-08-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.