2010/09/15 by Andrey Gogolev, Boris Kalinin, Gogolev, Andrey +3 · 1 citation
Mathematics · #37C15 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C15 #msc:37D20
paper · pdf · doi:10.48550/arxiv.1009.2994
18 pages, 2 figures, with an Appendix by Rafael de la Llave. Some minor fixes in the second version
arxiv created 2012/01/17 · arxiv updated 2012/01/18
We consider an irreducible Anosov automorphism L of a torus Td such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C1 conjugate to any C1-small perturbation f with the same periodic data. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d,Z). Examples constructed in the Appendix by Rafael de la Llave show importance of the assumption on the eigenvalues.