Non-invertible dynamical systems. Volume 1 : Ergodic theory - finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding m / Mariusz Urbański, Mario Roy, Sara Munday.

Format:

Book

Author/Creator:

Urbański, Mariusz, author.

Munday, Sara (Sara Ann), author.

Roy, Mario (Mathematics professor), author.

Series:

De Gruyter expositions in mathematics ; Volume 69/1.

De Gruyter expositions in mathematics ; Volume 69/1

Language:

English

Subjects (All):

Ergodic theory.

Physical Description:

1 online resource (458 pages)

Place of Publication:

Berlin, Germany : Walter de Gruyter GmbH, [2022]

Summary:

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.

Contents:

Frontmatter

Preface

List of Figures

Introduction to Volume 1

Contents

1 Dynamical systems

2 Homeomorphisms of the circle

3 Symbolic dynamics

4 Distance expanding maps

5 (Positively) expansive maps

6 Shub expanding endomorphisms

7 Topological entropy

8 Ergodic theory

9 Measure-theoretic entropy

10 Infinite invariant measures

11 Topological pressure

12 The variational principle and equilibrium states

Appendix A. A selection of classical results

Bibliography

Index

Notes:

Includes bibliographical references and index.

Current Copyright Fee: GBP22.50 0.

Description based on print version record.

ISBN:

9783110702682

3110702681

OCLC:

1286806634