Local rigidity for Anosov automorphisms

Andrey Gogolev, Boris Kalinin, Victoria Sadovskaya

Published 2010-09-15, updated 2012-01-17Version 2

We consider an irreducible Anosov automorphism L of a torus T^d such that no three eigenvalues have the same modulus. We show that L is locally rigid, that is, L is C^1 conjugate to any C^1-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.