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arXiv:1706.08505 [math.DS]AbstractReferencesReviewsResources

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

Lucas Backes, Mauricio Poletti, Adriana Sánchez

Published 2017-06-26Version 1

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.

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