On the ergodicity of geodesic flows on surfaces without focal points
On the ergodicity of geodesic flows on surfaces without focal points
复制标题
DOI：
10.1017/etds.2022.114
复制
发表时间：
2018-12
影响因子：
0.9
通讯作者：
Weisheng Wu;Fei Liu;Fang Wang
中科院分区：
文献类型：
--
作者：
Weisheng Wu;Fei Liu;Fang Wang
摘要本文研究了无焦点曲面上测地线流的遍历性。设M为光滑连通的封闭曲面，具有$C^{\infty }$黎曼度规g，其属$\mathfrak {g} \geq 2$。假设$(M,g)$没有焦点。我们证明了M的单位切线束上的测地线流相对于刘维尔测度是遍历的，假设M上具有负曲率的点的集合最多有有限个连通分量。
Abstract In this paper, we study the ergodicity of the geodesic flows on surfaces with no focal points. Let M be a smooth connected and closed surface equipped with a $C^{\infty }$ Riemannian metric g, whose genus $\mathfrak {g} \geq 2$ . Suppose that $(M,g)$ has no focal points. We prove that the geodesic flow on the unit tangent bundle of M is ergodic with respect to the Liouville measure, under the assumption that the set of points on M with negative curvature has at most finitely many connected components.