Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
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Anosov 流的可微性、刚性和 Godbillon-Vey 类
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
A. Katok
中科院分区：
文献类型：
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作者：
S. Hurder;A. Katok
紧流形上的安诺索夫动力系统的中心几何对象是不变的稳定叶状和不稳定叶状。虽然每个稳定的和不稳定的流形都和系统本身一样光滑，但它们形成的叶状结构被认为对大多数系统只有中等程度的规律性。我们将分析低维系统的余维一稳定叶和不稳定叶的精确正则度。我们的主要结果将这些叶的正则性与系统相关的上同类联系起来：本文引入的Anosov类是流的一个新的不变量，而弱稳定叶的Godbillon-Vey类是系统的一个定义良好的不变量
The central geometric objects associated with an Anosov dynamical system on a compact manifold are the invariant stable and unstable foliations. While each stable and unstable manifold is as smooth as the system itself, the foliations that they form are believed to have only a moderate degree of regularity for most systems. We will analyze the exact degree of regularity of codimension-one stable and unstable foliations for low dimensional systems. Our main results relate the regularity of these foliations to cohomology classes associated to the system: the Anosov class, a new invariant of the flow which we introduce in this paper, and the Godbillon-Vey class of the weak-stable foliations, which we show is a well-defined invariant of the system