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arXiv · 1909.11457

Flexibility of Lyapunov exponents with respect to two classes of measures on the torus

Alena Erchenko
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Abstract

We consider a smooth area-preserving Anosov diffeomorphism $f\colon \mathbb T^2\rightarrow \mathbb T^2$ homotopic to an Anosov automorphism $L$ of $\mathbb T^2$. It is known that the positive Lyapunov exponent of $f$ with respect to the normalized Lebesgue measure is less than or equal to the topological entropy of $L$, which, in addition, is less than or equal to the Lyapunov exponent of $f$ with respect to the probability measure of maximal entropy. Moreover, the equalities only occur simultaneously. We show that these are the only restrictions on these two dynamical invariants.

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Alena Erchenko. 2019-09-25. Flexibility of Lyapunov exponents with respect to two classes of measures on the torus. https://arxiv.org/abs/1909.11457

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