An Introduction To Infinite Ergodic Theory PDF Download
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Author | : Jon Aaronson |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821804944 |
Download An Introduction to Infinite Ergodic Theory Book in PDF, ePub and Kindle
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
Author | : Marc Kesseböhmer |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 204 |
Release | : 2016-10-10 |
Genre | : Mathematics |
ISBN | : 3110430851 |
Download Infinite Ergodic Theory of Numbers Book in PDF, ePub and Kindle
By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents: Preface Mathematical symbols Number-theoretical dynamical systems Basic ergodic theory Renewal theory and α-sum-level sets Infinite ergodic theory Applications of infinite ergodic theory Bibliography Index
Author | : Mariusz Urbański |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 458 |
Release | : 2021-11-22 |
Genre | : Mathematics |
ISBN | : 3110702681 |
Download Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps Book in PDF, ePub and Kindle
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.
Author | : Marc Kesseböhmer |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 204 |
Release | : 2016-10-10 |
Genre | : Mathematics |
ISBN | : 3110439425 |
Download Infinite Ergodic Theory of Numbers Book in PDF, ePub and Kindle
By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents: Preface Mathematical symbols Number-theoretical dynamical systems Basic ergodic theory Renewal theory and α-sum-level sets Infinite ergodic theory Applications of infinite ergodic theory Bibliography Index
Author | : Peter Walters |
Publisher | : Springer Science & Business Media |
Total Pages | : 268 |
Release | : 2000-10-06 |
Genre | : Mathematics |
ISBN | : 9780387951522 |
Download An Introduction to Ergodic Theory Book in PDF, ePub and Kindle
The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.
Author | : Giuseppe Da Prato |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2006-08-25 |
Genre | : Mathematics |
ISBN | : 3540290214 |
Download An Introduction to Infinite-Dimensional Analysis Book in PDF, ePub and Kindle
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
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 | : Karma Dajani |
Publisher | : CRC Press |
Total Pages | : 268 |
Release | : 2021-07-04 |
Genre | : Mathematics |
ISBN | : 1000402770 |
Download A First Course in Ergodic Theory Book in PDF, ePub and Kindle
A First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authors’ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from — designed to require only minimal prerequisites. Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented.
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 | : I︠A︡kov Grigorʹevich Sinaĭ |
Publisher | : Princeton University Press |
Total Pages | : 156 |
Release | : 1976 |
Genre | : Ergodic theory |
ISBN | : 9780691081823 |
Download Introduction to Ergodic Theory Book in PDF, ePub and Kindle