The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open


Abstract in English

We prove that the set of fiber-bunched $SL(2,mathbb{R})$-valued H{o}lder 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.

Download