Prevalence of a dominated splitting for cocycles with values in the semigroup of stochastic matrices

Details Prevalence of a dominated splitting for cocycles with values in the semigroup of stochastic matrices Prevalence of a dominated splitting for cocycles with values in the semigroup of stochastic matrices

2011-08-18

arxiv.org/abs/1108.3746v2

Mathematics

Dynamical Systems

Scientific paper

We prove that for a C^0-residual set of stochastic matrices over an ergodic automorphism, the splitting into points with 0 and negative Lyapunov exponent is dominated. Furthermore, if the Lyapunov spectrum contains at least three points, then the Oseledets splitting is dominated and, in particular, the Lyapunov exponents vary continuously. This result extends the dichotomy established by Bochi and Viana to a class of non-accessible cocycles.

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