Simplicity of Lyapunov spectra: a sufficient criterion

Details Simplicity of Lyapunov spectra: a sufficient criterion Simplicity of Lyapunov spectra: a sufficient criterion

2006-07-28

arxiv.org/abs/math/0607757v1

Mathematics

Dynamical Systems

47 pages

Scientific paper

We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h-Raugi and Gol'dsheid-Margulis, who considered products of random matrices, and of Bonatti-Viana, who dealt with the case when the base dynamics is a subshift of finite type. Here the Markov structure may have infinitely many symbols and the ambient space needs not be compact. As an application, in another paper we prove the Zorich-Kontsevich conjecture on the Lyapunov spectrum of the Teichm\"uller flow in the space of translation surfaces.

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