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arXiv · 1802.08266

Lyapunov exponents and rigidity of Anosov automorphisms and skew products

Radu Saghin·Jiagang Yang
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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.

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Radu Saghin, Jiagang Yang. 2018-02-22. Lyapunov exponents and rigidity of Anosov automorphisms and skew products. https://arxiv.org/abs/1802.08266

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