An Introduction to Infinite Ergodic Theory
Title | An Introduction to Infinite Ergodic Theory PDF eBook |
Author | Jon Aaronson |
Publisher | American Mathematical Soc. |
Total Pages | 298 |
Release | 1997 |
Genre | Mathematics |
ISBN | 0821804944 |
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.
Infinite Ergodic Theory of Numbers
Title | Infinite Ergodic Theory of Numbers PDF eBook |
Author | Marc Kesseböhmer |
Publisher | Walter de Gruyter GmbH & Co KG |
Total Pages | 230 |
Release | 2016-10-10 |
Genre | Mathematics |
ISBN | 3110430851 |
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
Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps
Title | Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps PDF eBook |
Author | Mariusz Urbański |
Publisher | Walter de Gruyter GmbH & Co KG |
Total Pages | 458 |
Release | 2021-11-22 |
Genre | Mathematics |
ISBN | 3110702681 |
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.
An Introduction to Ergodic Theory
Title | An Introduction to Ergodic Theory PDF eBook |
Author | Peter Walters |
Publisher | Springer Science & Business Media |
Total Pages | 268 |
Release | 2000-10-06 |
Genre | Mathematics |
ISBN | 9780387951522 |
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.
Lectures on Ergodic Theory
Title | Lectures on Ergodic Theory PDF eBook |
Author | Paul R. Halmos |
Publisher | Courier Dover Publications |
Total Pages | 112 |
Release | 2017-11-15 |
Genre | Mathematics |
ISBN | 0486826848 |
This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.
An Introduction to Infinite-Dimensional Analysis
Title | An Introduction to Infinite-Dimensional Analysis PDF eBook |
Author | Giuseppe Da Prato |
Publisher | Springer Science & Business Media |
Total Pages | 217 |
Release | 2006-08-25 |
Genre | Mathematics |
ISBN | 3540290214 |
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.
A First Course in Ergodic Theory
Title | A First Course in Ergodic Theory PDF eBook |
Author | Karma Dajani |
Publisher | CRC Press |
Total Pages | 268 |
Release | 2021-07-04 |
Genre | Mathematics |
ISBN | 1000402770 |
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.