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Local rigidity of Lyapunov spectrum for toral automorphisms

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    Andrey Gogolev

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Boris Kalinin & Victoria Sadovskaya

Authors
  1. Andrey Gogolev
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  2. Boris Kalinin
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  3. Victoria Sadovskaya
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Corresponding author

Correspondence to Andrey Gogolev.

Additional information

Supported in part by NSF grant DMS-1823150.

Supported in part by Simons Foundation grant 426243.

Supported in part by NSF grant DMS-1764216.

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Gogolev, A., Kalinin, B. & Sadovskaya, V. Local rigidity of Lyapunov spectrum for toral automorphisms. Isr. J. Math. 238, 389–403 (2020). https://doi.org/10.1007/s11856-020-2028-6

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  • DOI: https://doi.org/10.1007/s11856-020-2028-6

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