Continuity of Lyapunov exponents in all Hölder topologies for irreducible cocycles

Abstract

We prove that a locally constant $S{L}_2(\mathbb{R})$-valued cocycle over the shift generated by an irreducible collection of matrices is a continuity point for Lyapunov exponents in the $\alpha$-Hölder 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 $G{L}_2(\mathbb{R})$-valued cocycles that admit canonical holonomies.

The claim of Lemma 9.3 in the paper is false. The statement of the lemma can be corrected, however the corrected form is insufficient to deduce the claimed results

References in corpus (1)

• Discontinuity of Lyapunov Exponents Near Fiber Bunched Cocycles