Genericity of zero Lyapunov exponents

Details Genericity of zero Lyapunov exponents Genericity of zero Lyapunov exponents

2002-02-22

arxiv.org/abs/math/0202233v1

Ergodic Theory and Dynamical Systems, 22 (2002), 1667-1696

Mathematics

Dynamical Systems

28 pages, 1 figure. This is a revised, more readable, version of the preprint distributed in 2000

Scientific paper

10.1017/S0143385702001165

We show that, for any compact surface, there is a residual (dense $G_\delta$) set of $C^1$ area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mane, 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.

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