Symbolic dynamics for nonuniformly hyperbolic maps with singularities in high dimension / Ermerson Araujo, Yuri Lima, Mauricio Poletti.

Format:

Book

Author/Creator:

Araujo, Ermerson, author.

Lima, Yuri, author.

Poletti, Mauricio, author.

Series:

Memoirs of the American Mathematical Society ; v. 1511.

Memoirs of the American Mathematical Society ; v. 1511

Language:

English

Subjects (All):

Dynamics.

Symplectic geometry.

Physical Description:

v, 117 pages : illustrations ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2024

Summary:

We construct Markov partitions for non-invertible and/or singular nonuniformly hyperbolic systems defined on higher dimensional Riemannian manifolds. The generality of the setup covers classical examples not treated so far, such as geodesic flows in closed manifolds, multidimensional billiard maps, and Viana maps, and includes all the recent results of the literature. We also provide a wealth of applications.

Contents:

Chapter 1. Introduction

Chapter 2. Preliminaries

Part 1. Proof of the main theorem : Chapter 3. Pesin theory

Chapter 4. Overlap, double charts, and graph transforms

Chapter 5. Coarse graining

Chapter 6. The inverse problem

Chapter 7. Symbolic dynamics

Part 2. Applications : Chapter 8. Equilibrium measures

Chapter 9. Exponential growth rate of periodic orbits

Chapter 10. Flows with positive speed

Chapter 11. Multidimensional billiards

Chapter 12. Viana maps

Appendix A. The graph transform method

Bibliography.

Notes:

"September 2024 ; vol. 301 number 1511 (fifth of 7 numbers)".

Includes bibliographical references (pages 113-117).

ISBN:

1470471337

9781470471330

OCLC:

1467673758