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arXiv · 2208.03575

Upper bound on the regularity of the Lyapunov exponent for random products of matrices

Jamerson Bezerra·Pedro Duarte
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Abstract

We prove that if $\mu$ is a finitely supported measure on $\text{SL}_2(\mathbb{R})$ with positive Lyapunov exponent but not uniformly hyperbolic, then the Lyapunov exponent function is not $\alpha$-H\"older around $\mu$ for any $\alpha$ exceeding the Shannon entropy of $\mu$ over the Lyapunov exponent of $\mu$.

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Jamerson Bezerra, Pedro Duarte. 2022-08-06. Upper bound on the regularity of the Lyapunov exponent for random products of matrices. https://arxiv.org/abs/2208.03575

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