Local rigidity for Anosov automorphisms

Details Local rigidity for Anosov automorphisms Local rigidity for Anosov automorphisms

2010-09-15

arxiv.org/abs/1009.2994v2

Mathematics

Dynamical Systems

18 pages, 2 figures, with an Appendix by Rafael de la Llave. Some minor fixes in the second version

Scientific paper

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.

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