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

By:

Araujo, Ermerson [author.]

Contributor(s):

Material type: Text

TextSeries: Memoirs of the American Mathematical Society ; v. 1511.Publisher: Providence, Rhode Island : American Mathematical Society, 2024Copyright date: ©2024Description: v, 117 pages : illustrations ; 26 cmContent type:

text
still image

Media type:

unmediated

Carrier type:

volume

ISBN:

1470471337
9781470471330

Subject(s):

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.

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.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	Castorina	Coleções de Monografias (Monographs Collections)		1	Available		39063000810298

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

Includes bibliographical references (pages 113-117).

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.

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