Simplicity of the Lyapunov Spectrum for classes of Anosov flows
Abstract
We prove that in a C1-open and Ck-dense set of some classes of Ck Anosov flows all Lyapunov exponents have multiplicity 1 with respect to appropriate measures. The classes are geodesic flows with equilibrium states of H\"older-continuous potentials, volume-preserving flows, and all fiber-bunched Anosov flows with equilibrium states of H\"older-continuous potentials. In the proof, we use and prove perturbative results for jets of flows to modify eigenvalues of certain Poincar\'e maps and, using a Markov partition, apply the simplicity criterion of Avila and Viana.
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