Mathematics – Dynamical Systems
Scientific paper
2011-08-18
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.
Bessa Mario
Stadlbauer Manuel
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