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arXiv · 2604.09878

Discontinuity example for the Lyapunov exponents on the boundary of the uniformly hyperbolic set

Raquel Saraiva
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Abstract

We present an example of a discontinuity point for the Lyapunov exponents when viewed as a function of the cocycle in a topology finer than the $C^0$-topology. The linear cocycle taking values in SL(2,R) is locally constant, defined over a Bernoulli shift, and lies on the boundary of the uniformly hyperbolic set. In particular, we show that it can be approximated, in the $C_{\delta-\log}$-topology, by cocycles whose Lyapunov exponents vanish.

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Raquel Saraiva. 2026-04-10. Discontinuity example for the Lyapunov exponents on the boundary of the uniformly hyperbolic set. https://arxiv.org/abs/2604.09878

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