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arXiv · 2407.20310

Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles

Edhin Mamani·Raquel Saraiva
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Abstract

We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $\alpha$-H\"older topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli shift. Our example extends Bocker-Viana's and Butler's results. In particular, it gives a partial answer to a question raised by Clark Butler. Finally, we give an example of discontinuity in the setting of $SL(m,\mathbb{R})$-valued cocycles, which is constructed from $SL(2, \mathbb{R})$-valued cocycles.

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Edhin Mamani, Raquel Saraiva. 2024-07-29. Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles. https://arxiv.org/abs/2407.20310

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