arXiv subjects
Publications and source records attributed to Mauricio Poletti.
We prove that generic fiber-bunched and Hölder continuous linear cocycles over a non-uniformly hyperbolic system endowed with a u-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched cocycles.
We prove that the set of fiber-bunched $SL(2,\mathbb{R})$-valued Hölder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partially hyperbolic diffeomorphism is open. Moreover, we present an example showing that this is no longer true if we do not assume acessibility in the base dynamics.
In these notes we prove that the $s$ or $u$-states of cocycles over partially hyperbolic maps are closed in the space of invariant measures.
We prove that in an open and dense set, Symplectic linear cocycles over time one maps of Anosov flows, have positive Lyapunov exponents for SRB measures.
We prove that, for semi-invertible continuous cocycles, continuity of Lyapunov exponents is equivalent to continuity, in measure, of Oseledets subspaces.