Unique equilibrium states for geodesic flows over surfaces without focal points
Unique equilibrium states for geodesic flows over surfaces without focal points
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DOI：
10.1088/1361-6544/ab5c06
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发表时间：
2018-08
期刊：
影响因子：
1.7
通讯作者：
Dong Chen;Lien-Yung Kao;Kiho Park
中科院分区：
文献类型：
--
作者：
Dong Chen;Lien-Yung Kao;Kiho Park
本文研究亏格大于等于2的无焦点闭曲面上测地线流的动力学性质。特别地，我们证明了存在一类具有唯一平衡态的势，包括几何势的标量倍数，只要标量小于1。此外，我们讨论了这些独特的平衡态的遍历性质，包括伯努利性质和加权正则周期轨道相对于这些独特的平衡态是等分布的事实。
In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class of potentials having unique equilibrium states, including scalar multiples of the geometric potential, provided the scalar is less than 1. Moreover, we discuss ergodic properties of these unique equilibrium states, including the Bernoulli property and the fact that weighted regular periodic orbits are equidistributed relative to these unique equilibrium states.