On classification of resonance-free Anosov Z^k actions

2006/08/23 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +1
Mathematics · #37C15 #37C85 #37D20 (primary) #37D30 (secondary) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS #msc:37C15 #msc:37C85 #msc:37D20 #msc:37D30

paper · pdf · doi:10.48550/arxiv.math/0608562

20 pages. To appear in Michigan Mathematical Journal

arxiv created 2007/03/26 · arxiv updated 2009/12/01

Abstract

We consider actions of Z^k, k ≥ 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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