Lyapunov exponents and rigidity of Anosov automorphisms and skew products

RADU SAGHIN, Jiagang Yang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper we obtain local rigidity results for linear Anosov diffeomorphisms in terms of Lyapunov exponents. More specifically, we show that given an irreducible linear hyperbolic automorphism L with simple real eigenvalues with distinct absolute values, any small perturbation preserving the volume and with the same Lyapunov exponents is smoothly conjugate to L. We also obtain rigidity results for skew products over Anosov diffeomorphisms. Given a volume preserving partially hyperbolic skew product diffeomorphism f0 over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation f of f0 with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.

Original languageEnglish
Article number106764
JournalAdvances in Mathematics
Volume355
DOIs
StatePublished - 15 Oct 2019
Externally publishedYes

Keywords

  • Anosov diffeomorphism
  • Lyapunov exponents
  • Partially hyperbolic diffeomorphism
  • Rigidity

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