Simplicity of the Lyapunov spectrum for classes of Anosov flows

Abstract

Abstract For $k \geq 2$ , we prove that in a $C^{1}$ -open and $C^{k}$ -dense set of some classes of $C^{k}$ -Anosov flows, all Lyapunov exponents have multiplicity one with respect to appropriate measures. The classes are geodesic flows with equilibrium states of Holder-continuous potentials, volume-preserving flows, and all fiber-bunched Anosov flows with equilibrium states of Holder-continuous potentials.

Locations

• Ergodic Theory and Dynamical Systems - View - PDF
• arXiv (Cornell University) - View - PDF
• Knowledge@UChicago (University of Chicago) - View - PDF