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On classification of resonance-free Anosov Z^k actions

Boris Kalinin·Victoria Sadovskaya
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Abstract

We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a finite cover of such an action is smoothly conjugate to an action by toral automorphisms.

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Boris Kalinin, Victoria Sadovskaya. 2007-03-26. On classification of resonance-free Anosov Z^k actions. https://arxiv.org/abs/math/0608562

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