The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open
Abstract
We prove that the set of fiber-bunched SL(2,R)-valued H\"older 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.
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