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arXiv · 2408.03878

Monochromatic nonuniform hyperbolicity

Jairo Bochi
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Abstract

We construct examples of continuous $\mathrm{GL}(2,\mathbb{R})$-cocycles which are not uniformly hyperbolic despite having the same non-zero Lyapunov exponents with respect to all invariant measures. The base dynamics can be any non-trivial subshift of finite type. According to a theorem of DeWitt--Gogolev and Guysinsky, such cocycles cannot be Hölder-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984.

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Jairo Bochi. 2025-09-12. Monochromatic nonuniform hyperbolicity. https://arxiv.org/abs/2408.03878

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