Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin, Vaughn Climenhaga

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)589-607
Number of pages19
JournalDiscrete and Continuous Dynamical Systems
Volume27
Issue number2
DOIs
StatePublished - Jun 1 2010

Fingerprint

Nonuniform Hyperbolicity
Open Problems
Dynamical systems
Genericity
Smooth Manifold
Coexistence
Compact Manifold
Attractor
Discrete-time
Dynamical system

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Open problems in the theory of non-uniform hyperbolicity. / Pesin, Yakov; Climenhaga, Vaughn.

In: Discrete and Continuous Dynamical Systems, Vol. 27, No. 2, 01.06.2010, p. 589-607.

Research output: Contribution to journalArticle

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