Positivity and simplicity of the Lyapunov spectrum for linear cocycles

Lundi 24 avril 10:15-11:45 - Mauricio Poletti - IMPA & Paris 13

Résumé : We consider Hölder continuous linear cocycles over a diffeomorphism with some hyperbolicity. Classical results of Avila, Bonatti and Viana prove that when the map is uniformly hyperbolic, generically (in the Hölder topology) the linear cocycles have non-zero Lyapunov exponents and moreover simple Lyapunov spectrum. We extend these results, relaxing the hyperbolicity condition to partial hyperbolicity and non-uniform hyperbolicity.

Positivity and simplicity of the Lyapunov spectrum for linear cocycles  Version PDF