Local rigidity of Lyapunov spectrum for toral automorphisms

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We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L4 is irreducible over ℚ. We consider a volume-preserving C1-small perturbation f of L. We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L, then f is C1+Hölder conjugate to L. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.

Original languageEnglish (US)
Pages (from-to)389-403
Number of pages15
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Jul 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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