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arXiv · 2503.21050

Random 2D linear cocycles I: dichotomic behavior

Pedro Duarte·Marcelo Durães·Tomé Graxinha·Silvius Klein
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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.

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Pedro Duarte, Marcelo Durães, Tomé Graxinha, Silvius Klein. 2025-03-26. Random 2D linear cocycles I: dichotomic behavior. https://arxiv.org/abs/2503.21050

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