Open problems in the theory of non-uniform hyperbolicity | Zendy

Yakov Pesin | Zendy; Vaughn Climenhaga | Zendy

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Open problems in the theory of non-uniform hyperbolicity

Author(s) -

Yakov Pesin,

Vaughn Climenhaga

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.27.589

Subject(s) - attractor , dissipative system , mathematics , pure mathematics , dynamical systems theory , mathematical analysis , physics , quantum mechanics

This is a survey-type article whose goal is to review some re- cent 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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