Preprint A04/2001
Genericity of zero Lyapunov exponents
Jairo Bochi
Keywords: Lyapunov Exponents | Anosov diffeomorphisms | area-preserving diffeomorphisms
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. Ma\~{n}\'{e}, 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 $\sl2r$-cocycles which either are uniformly hyperbolic or have zero exponents a.e.