On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces
On the equidistribution of unstable curves for pseudo-Anosov diffeomorphisms of compact surfaces
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致密曲面拟阿诺索夫微分同胚不稳定曲线的等分布
DOI：
10.1017/etds.2021.119
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发表时间：
2020
影响因子：
0.9
通讯作者：
G. Forni
中科院分区：
文献类型：
--
作者：
G. Forni
摘要证明了沿高属紧致可定向曲面上的全Anosov微分同构或伪Anosov微分同构的不变叶形遍历积分的渐近性（在对数误差范围内）是由微分同构对曲面上同调的作用决定的。由于我们的论点和Giulietti和Liverani[抛物动力学和各向异性巴拿赫空间]的结果。j .欧元。数学。Soc。在全球平均上，所有Anosov微分同态在开放区间内不存在Ruelle共振(JEMS, 21（9) (2019), 2793-2858）
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
$(1, e^{h_{\mathrm {top}}})$
.