Lyapunov exponents and rigidity of Anosov automorphisms and skew products

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 $f_0$ over an Anosov automorphism of the 2-torus, we show that for any volume preserving perturbation $f$ of $f_0$ with the same average stable and unstable Lyapunov exponents, the center foliation is smooth.

improved version

References in corpus (2)

• On conservative partially hyperbolic abelian actions with compact center foliation
• Decay of correlations for maximal measure of maps derived from Anosov

Cited by in corpus (2)

• Characterizing symmetric spaces by their Lyapunov spectra
• Local rigidity of certain solvable group actions on tori