Random 2D linear cocycles I: dichotomic behavior
Dynamical Systems
2025-03-28 v1 Mathematical Physics
math.MP
Abstract
In this paper we establish a Bochi-Ma\~n\'e type dichotomy in the space of two dimensional, nonnegative determinant matrix valued, locally constant linear cocycles over a Bernoulli or Markov shift. Moreover, we prove that Lebesgue almost every such cocycle has finite first Lyapunov exponent, which then implies a break in the regularity of the Lyapunov exponent, from analyticity to discontinuity.
Keywords
Cite
@article{arxiv.2503.21050,
title = {Random 2D linear cocycles I: dichotomic behavior},
author = {Pedro Duarte and Marcelo Durães and Tomé Graxinha and Silvius Klein},
journal= {arXiv preprint arXiv:2503.21050},
year = {2025}
}
Comments
33 pages