Unique Equilibrium States for Geodesic Flows on Flat Surfaces with Singularities
Unique Equilibrium States for Geodesic Flows on Flat Surfaces with Singularities
复制标题
具有奇点的平坦表面上测地流的独特平衡态
DOI：
10.1093/imrn/rnac247
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发表时间：
2022
影响因子：
1
通讯作者：
Work, Grace
中科院分区：
文献类型：
--
作者：
Call, Benjamin;Constantine, David;Erchenko, Alena;Sawyer, Noelle;Work, Grace
考虑一个紧致的平面，它具有一个度规，除了有有限多个角度大于。根据Burns、Climenhaga、Fisher和Thompson的工作，我们证明了在奇异集不支持全压力的情况下，充分正则势函数具有唯一的平衡态。此外，我们证明了压力间隙对奇异集的邻域上的任何局部常数势都成立。最后，我们建立了相应的平衡态具有闭正则测地线等分布的性质。
Consider a compact surface of genusequipped with a metric that is flat everywhere except at finitely many cone points with angles greater than. Following the technique in the work of Burns, Climenhaga, Fisher, and Thompson, we prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not support the full pressure. Moreover, we show that the pressure gap holds for any potential that is locally constant on a neighborhood of the singular set. Finally, we establish that the corresponding equilibrium states have the-property and closed regular geodesics equidistribute.