论文标题
大地测量的Anosov流动，双曲线封闭的大地测量和稳定的磨性
Geodesic Anosov flows, hyperbolic closed geodesics and stable ergodicity
论文作者
论文摘要
在本文中，我们表明，只有存在$ c^2 $开放的Finsler指标，所有其封闭的大地测量学都是双曲线的，且仅当存在一个$ c^2 $开放式街区时，芬斯勒指标的大地测量流量是Anosov。对于Riemannian指标，此结果也成立。这是基于Contreras和Mazzucchelli的最新结果。此外，Riemannian或Finsler在表面上的测量流量是$ C^2 $稳定的，并且仅在它们是Anosov时。
In this paper we show that the geodesic flow of a Finsler metric is Anosov if and only if there exists a $C^2$ open neighborhood of Finsler metrics all of whose closed geodesics are hyperbolic. For surfaces this result holds also for Riemannian metrics. This follows from a recent result of Contreras and Mazzucchelli. Furthermore, geodesic flows of Riemannian or Finsler metrics on surfaces are $C^2$ stably ergodic if and only if they are Anosov.
