We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Hölder potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the pressure gap condition. Moreover, we derive several ergodic properties of the unique equilibrium states including the equidistribution and the K-property.

中文翻译：

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没有焦点的流形上测地线流的平衡态性质

我们证明，对于没有焦点的封闭1级流形，平衡状态对于满足压力差条件的Hölder势而言是唯一的。此外，我们提供了满足电位差条件的连续电位的标准。此外，我们得出了独特平衡态的若干遍历性质，包括均分布和K属性。