Lyapunov exponents and rigidity of Anosov automorphisms and skew products

Resumen

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 spectrum, 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.

Autores: R. Saghin, J. Yang,

URL de la publicación: https://arxiv.org/abs/1802.08266