Ruelle spectrum of linear pseudo-Anosov maps
Ruelle spectrum of linear pseudo-Anosov maps
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线性伪阿诺索夫映射的 Ruelle 谱
DOI：
10.5802/jep.107
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Erwan Lanneau
中科院分区：
文献类型：
--
作者：
F. Faure;S. Gouezel;Erwan Lanneau
动力系统的 Ruelle 共振是描述相关性的精确渐近的谱数据。我们根据映射对上同调的作用将它们完全分类为一类混沌二维映射，即线性伪阿诺索夫映射。作为应用，我们获得了在线性伪阿诺索夫映射的稳定方向上线性流下不变的分布的完整描述，并求解了该流的上同调方程。
The Ruelle resonances of a dynamical system are spectral data describing the precise asymptotics of correlations. We classify them completely for a class of chaotic two-dimensional maps, the linear pseudo-Anosov maps, in terms of the action of the map on cohomology. As applications, we obtain a full description of the distributions which are invariant under the linear flow in the stable direction of such a linear pseudo-Anosov map, and we solve the cohomological equation for this flow.