Dynamical Systems Ergodic Theory And Probability

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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

Smooth Ergodic Theory of Random Dynamical Systems

Author : Pei-Dong Liu
Publisher : Springer
ISBN 13 : 3540492917
Total Pages : 233 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Smooth Ergodic Theory of Random Dynamical Systems by : Pei-Dong Liu

Download or read book Smooth Ergodic Theory of Random Dynamical Systems written by Pei-Dong Liu and published by Springer. This book was released on 2006-11-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Ergodic Theory and Differentiable Dynamics

Author : Ricardo Mane
Publisher : Springer Science & Business Media
ISBN 13 : 3642703356
Total Pages : 328 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Ergodic Theory and Differentiable Dynamics by : Ricardo Mane

Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

Ergodic Dynamics

Author : Jane Hawkins
Publisher : Springer Nature
ISBN 13 : 3030592421
Total Pages : 340 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Ergodic Dynamics by : Jane Hawkins

Download or read book Ergodic Dynamics written by Jane Hawkins and published by Springer Nature. This book was released on 2021-01-28 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical Systems, Ergodic Theory, and Probability

Author : Alexander M. Blokh
Publisher :
ISBN 13 : 9781470442248
Total Pages : 316 pages
Book Rating : 4.4/5 (422 download)

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Book Synopsis Dynamical Systems, Ergodic Theory, and Probability by : Alexander M. Blokh

Download or read book Dynamical Systems, Ergodic Theory, and Probability written by Alexander M. Blokh and published by . This book was released on 2017 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Dynamical Systems, Ergodic Theory, and Probability, which was dedicated to the memory of Nikolai Chernov, held from May 18-20, 2015, at the University of Alabama at Birmingham, Birmingham, Alabama. The book is devoted to recent advances in the theory of chaotic and weakly chaotic dynamical systems and its applications to statistical mechanics. The papers present new original results as well as comprehensive surveys.

Ergodic Theory

Author : I. P. Cornfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1461569273
Total Pages : 487 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Ergodic Theory by : I. P. Cornfeld

Download or read book Ergodic Theory written by I. P. Cornfeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.

Ergodic Theory via Joinings

Author : Eli Glasner
Publisher : American Mathematical Soc.
ISBN 13 : 1470419513
Total Pages : 402 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ergodic Theory via Joinings by : Eli Glasner

Download or read book Ergodic Theory via Joinings written by Eli Glasner and published by American Mathematical Soc.. This book was released on 2015-01-09 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author : Bernold Fiedler
Publisher : Springer Science & Business Media
ISBN 13 : 3642565891
Total Pages : 816 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Ergodic Theory and Statistical Mechanics

Author : Jean Moulin Ollagnier
Publisher : Springer
ISBN 13 : 3540392890
Total Pages : 154 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Ergodic Theory and Statistical Mechanics by : Jean Moulin Ollagnier

Download or read book Ergodic Theory and Statistical Mechanics written by Jean Moulin Ollagnier and published by Springer. This book was released on 2007-01-05 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory and Differentiable Dynamics

Author : Ricardo Mañé
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Ergodic Theory and Differentiable Dynamics by : Ricardo Mañé

Download or read book Ergodic Theory and Differentiable Dynamics written by Ricardo Mañé and published by Springer. This book was released on 1987 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to ergodic theory, with an emphasis on its relationship with the theory of differentiable dynamical systems, sometimes called differentiable ergodic theory. The first chapter a quick review of measure theory is included as a reference.

Dynamical Systems and Ergodic Theory

Author : Mark Pollicott
Publisher : Cambridge University Press
ISBN 13 : 9780521575997
Total Pages : 198 pages
Book Rating : 4.5/5 (759 download)

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Book Synopsis Dynamical Systems and Ergodic Theory by : Mark Pollicott

Download or read book Dynamical Systems and Ergodic Theory written by Mark Pollicott and published by Cambridge University Press. This book was released on 1998-01-29 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).

Ergodic Theory

Author : Karl E. Petersen
Publisher : Cambridge University Press
ISBN 13 : 9780521389976
Total Pages : 348 pages
Book Rating : 4.3/5 (899 download)

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Book Synopsis Ergodic Theory by : Karl E. Petersen

Download or read book Ergodic Theory written by Karl E. Petersen and published by Cambridge University Press. This book was released on 1989-11-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.

Probability, Random Processes, and Ergodic Properties

Author : Robert M. Gray
Publisher : Springer Science & Business Media
ISBN 13 : 1475720246
Total Pages : 309 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Probability, Random Processes, and Ergodic Properties by : Robert M. Gray

Download or read book Probability, Random Processes, and Ergodic Properties written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature.

Ergodic Theory and Dynamical Systems

Author : Yves Coudène
Publisher : Springer
ISBN 13 : 1447172876
Total Pages : 192 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Ergodic Theory and Dynamical Systems by : Yves Coudène

Download or read book Ergodic Theory and Dynamical Systems written by Yves Coudène and published by Springer. This book was released on 2016-11-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov

Author : Alexander M. Blokh
Publisher : American Mathematical Soc.
ISBN 13 : 1470427737
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov by : Alexander M. Blokh

Download or read book Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov written by Alexander M. Blokh and published by American Mathematical Soc.. This book was released on 2017-09-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Dynamical Systems, Ergodic Theory, and Probability, which was dedicated to the memory of Nikolai Chernov, held from May 18–20, 2015, at the University of Alabama at Birmingham, Birmingham, Alabama. The book is devoted to recent advances in the theory of chaotic and weakly chaotic dynamical systems and its applications to statistical mechanics. The papers present new original results as well as comprehensive surveys.

Convergence in Ergodic Theory and Probability

Author : Vitaly Bergelson
Publisher : Walter de Gruyter
ISBN 13 : 3110889382
Total Pages : 461 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Convergence in Ergodic Theory and Probability by : Vitaly Bergelson

Download or read book Convergence in Ergodic Theory and Probability written by Vitaly Bergelson and published by Walter de Gruyter. This book was released on 2011-06-15 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.

Convexity in the Theory of Lattice Gases

Author : Robert B. Israel
Publisher : Princeton University Press
ISBN 13 : 1400868424
Total Pages : 257 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Convexity in the Theory of Lattice Gases by : Robert B. Israel

Download or read book Convexity in the Theory of Lattice Gases written by Robert B. Israel and published by Princeton University Press. This book was released on 2015-03-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. Originally published in 1979. 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.