On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces
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Abstract We prove that the asymptotics of ergodic integrals along an invariant foliation of a toral Anosov diffeomorphism, or of a pseudo-Anosov diffeomorphism on a compact orientable surface of higher genus, is 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 [Parabolic dynamics and anisotropic Banach spaces. J. Eur. Math. Soc. (JEMS)21(9) (2019), 2793–2858] on horospherical averages, toral Anosov diffeomorphisms have no Ruelle resonances in the open interval $(1, e^{h_{\mathrm {top}}})$ .
1995 ◽
Vol 15
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pp. 317-331
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2014 ◽
Vol 14
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pp. 1550002
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1991 ◽
Vol 11
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pp. 427-441
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1991 ◽
Vol 33
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pp. 213-221
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2004 ◽
Vol 56
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pp. 1228-1236
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