论文标题
共同学方程的ruelle共振
Ruelle resonances from cohomological equations
论文作者
论文摘要
这些笔记是基于作者在暑期学校对Teichmüller动态的讲座，在法国格雷诺布尔绘制班级和应用，并于2018年6月在Oberwolfach的研讨会上以及有关各向异性空间及其应用于2019年6月的双胞胎和抛物性系统的信息。相应的不稳定矢量场的共同体方程和不变分布的结果。特别是，我们考虑了较高属的表面上的伪anosov差异性，用于恒定负曲率表面上的骨流动，以及海森贝格3维nilmanfolds的部分双曲线自动形态。 F. Faure，S。Gouëzel和E. lanneau [FGL]深入研究了与配置不稳定翻译流相同的伪anosov图的Ruelles共振，并通过方法通过基于Pseudo-Anosov Map传输操作员的方法进行了深入研究。 Dyatlov，Faure和Guillarmou和Guillarmou [dfg]以及基于Emagical of Ofdods的一般结果，通过一般结果研究了Heisenberg 3维Nilmanfolds的任何维度和部分双曲自动形态的杂音共振的共振。这些作品并未为这些系统的不稳定流或霍斯氏叶的共同体方程取得结果。
These notes are based on lectures given by the author at the Summer School on Teichmüller dynamics, mapping class groups and applications in Grenoble, France, in June 2018 and at the Oberwolfach Seminar on Anisotropic Spaces and their Applications to Hyperbolic and Parabolic Systems in June 2019. We derive results about the so-called Ruelle resonances and the asymptotics of correlations for several classes of systems from known results on cohomological equations and invariant distributions for the respective unstable vector fields. In particular, we consider pseudo-Anosov diffeomorphisms on surfaces of higher genus, for horocycle flows on surfaces of constant negative curvature and for partially hyperbolic automorphisms of Heisenberg 3-dimensional nilmanfolds. Ruelles resonances for pseudo-Anosov maps with applications to the cohomological equation for their unstable translation flows was recently studied in depth by F. Faure, S. Gouëzel and E. Lanneau [FGL] by methods based on the analysis of the transfer operator of the pseudo-Anosov map. Ruelle resonances for geodesic flows on hyperbolic compact manifolds of any dimension and of partially hyperbolic automorphisms of Heisenberg 3-dimensional nilmanfolds are studied by general results of Dyatlov, Faure and Guillarmou [DFG] and Faure and Tsujii [FT15] based on methods of semi-classical analysis. These works do not derive results on cohomological equations for unstable flows or horospherical foliations of these systems.
