Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin, Vaughn Climenhaga

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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
Issue number2
StatePublished - Jun 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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