论文标题
Anosov的差异性，各向异性BV空间和叶子的规律性
Anosov diffeomorphisms, anisotropic BV spaces and regularity of foliations
论文作者
论文摘要
鉴于任何光滑的Anosov地图，我们构造了一个Banach空间，相关的传输操作员在其上是准连接的。这样一个空间的特殊性在于，在扩展地图的情况下，它将其完全降低到有界变化的通常功能空间，事实证明，在研究分段扩展地图的统计属性方面已特别成功。我们的方法是基于一种研究叶子的绝对连续性的新方法，该方法提供了新信息，这些信息可以证明可用于治疗具有奇异性的双曲线系统。
Given any smooth Anosov map we construct a Banach space on which the associated transfer operator is quasi-compact. The peculiarity of such a space is that in the case of expanding maps it reduces exactly to the usual space of functions of bounded variation which has proven particularly successful in studying the statistical properties of piecewise expanding maps. Our approach is based on a new method of studying the absolute continuity of foliations which provides new information that could prove useful in treating hyperbolic systems with singularities.
