Local rigidity for Anosov automorphisms

Andrey Gogolev, Boris Kalinin, Victoria Sadovskaya, Rafael De La Llave

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

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+Hölder1 conjugate to any C 1-small perturbation f such that the derivative Dpfn is conjugate to Ln whenever fnp = p. We also prove that toral automorphisms satisfying these assumptions are generic in SL(d, ℤ). Examples constructed in the Appendix show the importance of the assumption on the eigenvalues.

Original languageEnglish (US)
Pages (from-to)843-858
Number of pages16
JournalMathematical Research Letters
Volume18
Issue number5
DOIs
StatePublished - Sep 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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