Genericity of Zero Lyapunov Exponents
نویسنده
چکیده
We show that, for any compact surface, there is a residual (dense Gδ) set of C 1 area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé, but no proof was available. We also show that for any fixed ergodic dynamical system over a compact space, there is a residual set of continuous SL(2, R)-cocycles which either are uniformly hyperbolic or have zero exponents a.e.
منابع مشابه
Existence and Genericity Problems for Dynamical Systems with Nonzero Lyapunov Exponents
This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents. MSC2000 numbers: 58F09 DOI: 10.1134/S1560354707050024
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