On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces

Giovanni Forni

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arXiv · 2007.03144

On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces

Giovanni Forni

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Abstract

Weprovethattheasymptoticsofergodicintegralsalonganinvariant foliation of a toral Anosov diffeomorphism, or of a pseudo-Anosov diffeomorphism on a compact orientable surface of higher genus, are determined (up to a logarithmic error) by the action of the diffeomorphism on the cohomology of the surface. As a consequence of our argument and of the results of Giulietti and Liverani [GL] on horospherical averages, toral Anosov diffeomorphisms have no Ruelle resonances in the open interval $(1,e^{h_{top}} )$.

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Giovanni Forni. 2020-07-07. On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces. https://arxiv.org/abs/2007.03144

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