Year: 2015
Type: preprint
Abstract: In this paper we prove the continuity of all Lyapunov exponents, as well as the continuity of the Oseledets decomposition, for a class of irreducible cocycles over strongly mixing Markov shifts. Moreover, gaps in the Lyapunov spectrum lead to a Hölder modulus of continuity for these quantities. This result is an application of the abstract continuity theorems obtained in [4], and generalizes a theorem of E. Le Page on the Hölder continuity of the maximal LE for one-parameter families of strongly irreducible and contracting cocycles over a Bernoulli shift. This is a draft of a chapter in our forthcoming research monograph [4].
Source: arXiv (Cornell University)
Authors: Klein, Silvius, Duarte, Pedro
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W768454639