论文标题
负曲率中的沿阵牛式优化和零温度限制
Ergodic optimization and zero temperature limits in negative curvature
论文作者
论文摘要
在本文中，我们研究了非紧密弯曲的歧管上测量流的千古理论的各个方面。众所周知的事实是，紧凑型公制空间上的每个连续潜力都具有最大化的度量。不幸的是，对于非紧凑空间，这一事实并不长。对于地球流量，我们提供了一个标准，该标准可确保存在最大程度地衡量统一连续电位的措施。我们证明，最大化度量的唯一障碍是质量现象的完全逃脱。据我们所知，这是对非压缩拓扑空间的最大化措施的第一个总体结果，这不需要强制性。我们研究合适电位家族的平衡度量的零温度极限。我们证明了这种措施的限制行为有一些融合和分歧结果。在某些后果中，我们得到的是，测量流具有中间熵特性，并且平衡状态在不变概率度量的空间中密集。
In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a compact metric space has a maximizing measure. Unfortunately, for non-compact spaces this fact is not longer true. For the geodesic flow we provide a criterion that ensures the existence of a maximizing measure for uniformly continuous potentials. We prove that the only obstruction to the existence of a maximizing measure is the full escape of mass phenomenon. To the best of our knowledge, this is the first general result on the existence of maximizing measures for non-compact topological spaces which does not require the potential to be coercive. We study zero temperature limits of equilibrium measures for a suitable family of potentials. We prove some convergence and divergence results for the limiting behaviour of such measures. Among some consequences we obtain that the geodesic flow has the intermediate entropy property and that equilibrium states are dense in the space of invariant probability measures.
