2025/03/26 by Pedro Duarte, Duarte, Pedro, Marcelo Durães +5
Mathematics · #37H15 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2503.21050
openalex publication_date 2025/03/26 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
In this paper we establish a Bochi-Mañé 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.