We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hölder Jacobians. In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any probability (invariant or not) having conditionals given by this family, necessarily is the unique equilibrium state of the system.

中文翻译：

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对双曲流遍历理论的贡献：准不变测度的独特遍历性和一次映射的平衡状态

我们考虑对应于（拓扑混合）阿诺索夫流或微分同胚的环环流，并利用霍尔德雅可比行列式建立横向准不变测度的唯一性。在相同的设置中，我们给出了双曲系统平衡状态的精确表征，表明氡族的存在对星环叶状结构进行测量，使得具有该族给出的条件的任何概率（不变或不变）必然是系统的独特平衡状态。