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arXiv · 1909.08767

Continuity of Lyapunov exponents in all H\"older topologies for irreducible cocycles

Clark Butler
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Abstract

We prove that a locally constant $SL_{2}(\mathbb{R})$-valued cocycle over the shift generated by an irreducible collection of matrices is a continuity point for Lyapunov exponents in the $\alpha$-H\"older topology for every $\alpha > 0$. This gives negative answers to conjectures of Viana and the author; we pose a new conjecture to replace these conjectures. We show that an analogous continuity result also holds for $GL_{2}(\mathbb{R})$-valued cocycles that admit canonical holonomies.

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Clark Butler. 2019-09-19. Continuity of Lyapunov exponents in all H\"older topologies for irreducible cocycles. https://arxiv.org/abs/1909.08767

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