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arXiv · 1807.11335

Characterization of uniform hyperbolicity for fiber-bunched cocycles

Renato Velozo
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Abstract

We prove a new characterization of uniform hyperbolicity for fiber-bunched cocycles. Specifically, we show that the existence of a uniform gap between the Lyapunov exponents of a fiber-bunched $SL(2,\mathbb{R})$-cocycle defined over a subshift of finite type or an Anosov diffeomorphism implies uniform hyperbolicity. In addition, we construct an $\alpha$-H\"{o}lder cocycle which has uniform gap between the Lyapunov exponents, however it is not uniformly hyperbolic.

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Renato Velozo. 2018-07-30. Characterization of uniform hyperbolicity for fiber-bunched cocycles. https://arxiv.org/abs/1807.11335

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