论文标题
非阳性曲率中的hhosphers等分
Equidistribution of horospheres in nonpositive curvature
论文作者
论文摘要
我们研究了霍斯氏菌在具有非阳性曲率的等级1歧管上的厄法德特性。我们证明，在大量的歧管上，在大地摩尔古里斯测量的地球流动的作用下，将holosphers均等分配。在表面的情况下，我们定义了烟节流的参数化，该集合在大地测量流的作用下复发的horocycles集合。我们证明，限制到该集合的肉眼流是独特的。结果对于包括紧凑的歧管有效。
We study the ergodic properties of horospheres on rank 1 manifolds with non-positive curvature. We prove that the horospheres are equidistributed under the action of the geodesic flow towards the Bowen-Margulis measure, on a large class of manifolds. In the case of surfaces, we define a parametrization of the horocyclic flow on the set of horocycles containing a rank 1 vector that is recurrent under the action of the geodesic flow. We prove that the horocyclic flow in restriction to this set is uniquely ergodic. The results are valid for large classes of manifolds, including the compact ones.
