Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin; Vaughn Climenhaga

doi:10.3934/dcds.2010.27.589

Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin, Vaughn Climenhaga

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

This is a survey-type article whose goal is to review some recent developments in studying the genericity problem for non-uniformly hyperbolic dynamical systems with discrete time on compact smooth manifolds. We discuss both cases of systems which are conservative (preserve the Riemannian volume) and dissipative (possess hyperbolic attractors). We also consider the problem of coexistence of hyperbolic and regular behaviour.

Original language	English (US)
Pages (from-to)	589-607
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems
Volume	27
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2010.27.589
State	Published - Jun 2010

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2010.27.589

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AB - This is a survey-type article whose goal is to review some recent developments in studying the genericity problem for non-uniformly hyperbolic dynamical systems with discrete time on compact smooth manifolds. We discuss both cases of systems which are conservative (preserve the Riemannian volume) and dissipative (possess hyperbolic attractors). We also consider the problem of coexistence of hyperbolic and regular behaviour.

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Open problems in the theory of non-uniform hyperbolicity

Abstract

All Science Journal Classification (ASJC) codes

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