# American Institute of Mathematical Sciences

May  2010, 27(2): 589-607. doi: 10.3934/dcds.2010.27.589

## Open problems in the theory of non-uniform hyperbolicity

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

Received  October 2009 Revised  February 2010 Published  February 2010

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.
Citation: Yakov Pesin, Vaughn Climenhaga. Open problems in the theory of non-uniform hyperbolicity. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 589-607. doi: 10.3934/dcds.2010.27.589
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