Foundations Of Ergodic Theory PDF Download
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Author | : Marcelo Viana |
Publisher | : Cambridge University Press |
Total Pages | : 547 |
Release | : 2016-02-15 |
Genre | : Mathematics |
ISBN | : 1107126967 |
Download Foundations of Ergodic Theory Book in PDF, ePub and Kindle
Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.
Author | : Marcelo Viana |
Publisher | : Cambridge University Press |
Total Pages | : 547 |
Release | : 2016-02-15 |
Genre | : Mathematics |
ISBN | : 1316445429 |
Download Foundations of Ergodic Theory Book in PDF, ePub and Kindle
Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.
Author | : Karl E. Petersen |
Publisher | : Cambridge University Press |
Total Pages | : 348 |
Release | : 1989-11-23 |
Genre | : Mathematics |
ISBN | : 9780521389976 |
Download Ergodic Theory Book in PDF, ePub and Kindle
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.
Author | : Daniel J. Rudolph |
Publisher | : Oxford University Press, USA |
Total Pages | : 190 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Fundamentals of Measurable Dynamics Book in PDF, ePub and Kindle
This book is designed to provide graduate students and other researchers in dynamical systems theory with an introduction to the ergodic theory of Lebesgue spaces. The author's aim is to present a technically complete account which offers an in-depth understanding of the techniques of the field, both classical and modern. Thus, the basic structure theorems of Lebesgue spaces are given in detail as well as complete accounts of the ergodic theory of a single transformation, ergodic theorems, mixing properties and entropy. Subsequent chapters extend the earlier material to the areas of joinings and representation theorems, in particular the theorems of Ornstein and Krieger. Prerequisites are a working knowledge of Lebesgue measure and the topology of the real line as might be gained from the first year of a graduate course. Many exercises and examples are included to illustrate and to further cement the reader's understanding of the material. The result is a text which will furnish the reader with a sound technical background from the foundations of the subject to some of its most recent developments.
Author | : Eli Glasner |
Publisher | : American Mathematical Soc. |
Total Pages | : 402 |
Release | : 2015-01-09 |
Genre | : Mathematics |
ISBN | : 1470419513 |
Download Ergodic Theory via Joinings Book in PDF, ePub and Kindle
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.
Author | : I. P. Cornfeld |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461569273 |
Download Ergodic Theory Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 25 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download Ergodic Theory and the Foundations of Statistical Mechanics Book in PDF, ePub and Kindle
Author | : Aleksandr I?Akovlevich Khinchin |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 1957-01-01 |
Genre | : Mathematics |
ISBN | : 0486604349 |
Download Mathematical Foundations of Information Theory Book in PDF, ePub and Kindle
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.
Author | : Karl E. Petersen |
Publisher | : Cambridge University Press |
Total Pages | : 343 |
Release | : 1989-11-23 |
Genre | : Mathematics |
ISBN | : 1316583201 |
Download Ergodic Theory Book in PDF, ePub and Kindle
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.
Author | : R. Jancel |
Publisher | : Elsevier |
Total Pages | : 441 |
Release | : 2013-10-22 |
Genre | : Science |
ISBN | : 1483186261 |
Download Foundations of Classical and Quantum Statistical Mechanics Book in PDF, ePub and Kindle
Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.