单色非均匀双曲性

arXiv - MATH - Dynamical Systems Pub Date : 2024-08-07 DOI:arxiv-2408.03878

Jairo Bochi

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引用次数: 0

摘要

我们构造了连续 $\mathrm{GL}(2,\mathbb{R})$ 循环的例子，这些循环尽管相对于所有不变度量具有相同的非零 Lyapunovexponents，却不是均匀双曲的。基动力学可以是有限类型的任何非三维子移动。根据DeWitt--Gogolevand Guysinsky的定理，这样的cocycles不可能是连续的。我们的构造使用了沃尔特斯在 1984 年发现的非均匀双曲循环。

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Monochromatic nonuniform hyperbolicity

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 H\"older-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984.

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arXiv - MATH - Dynamical Systems

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