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

Published 29 Jul 2024 in math.DS | (2407.20310v1)

Abstract: We exhibit an example of a discontinuity point for the Lyapunov exponents as a function of the cocycle in the 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.

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