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arXiv · 1706.08505

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

Lucas Backes·Mauricio Poletti·Adriana Sánchez
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Abstract

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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Lucas Backes, Mauricio Poletti, Adriana Sánchez. 2017-06-26. The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open. https://doi.org/10.4310/mrl.2018.v25.n6.a2

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