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arXiv · 2212.00174

H\"older continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula

Ao Cai·Marcelo Durães·Silvius Klein·Aline Melo
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Abstract

This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint H\"older continuity of the maximal Lyapunov exponent as a function of the cocycle and the transition kernel in the vicinity of any irreducible cocycle with simple maximal Lyapunov exponent. Our approach, via Furstenberg's formula, shows the H\"older continuous dependence on the data of the stationary measure of the projective cocycle and in particular provides a more computable H\"older exponent.

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Ao Cai, Marcelo Durães, Silvius Klein, Aline Melo. 2022-11-30. H\"older continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula. https://arxiv.org/abs/2212.00174

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