Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin; Vaughn Climenhaga

doi:10.3934/dcds.2010.27.589

Article Contents

2010, Volume 27, Issue 2: 589-607. Doi: 10.3934/dcds.2010.27.589

This issue Previous Article One-dimensional dynamics in the new millennium Next Article Rigidity of real-analytic actions of $SL(n,\Z)$ on $\T^n$: A case of realization of Zimmer program

Open problems in the theory of non-uniform hyperbolicity

Yakov Pesin^1, and
Vaughn Climenhaga^1,

1.
Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802

Received: September 30, 2009

Revised: January 31, 2010

Published: June 2010

Abstract Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: Primary: 37-02, 37D25, 37C20; Secondary: 37A10, 37D30.

Citation:

Article Metrics

HTML views() PDF downloads(116) Cited by(0)

Open problems in the theory of non-uniform hyperbolicity

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Open problems in the theory of non-uniform hyperbolicity

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content