标题： 热力学形式化对于准同态：有界上同调和统计学 显示英文标题

标题： Thermodynamic formalism for Quasi-Morphisms: Bounded Cohomology and Statistics

摘要： 对于紧致负曲率空间，我们发展了一种热力学形式主义，并将其应用于研究其基本群模有界性的拟同态空间。 我们证明该空间与对应于相关Gromov测地流的Bowen函数空间在模一个弱的Livsic上同调意义下是Banach同构的。 结果包括每个这样的无界拟同态都与流的一个唯一不变测度相关联，并且该测度唯一地决定了上同调类。 作为推论，我们建立了任何无界拟同态相对于马尔可夫测度的中心极限定理、不变性原理以及相关平衡态的伯努利性质。 显示英文摘要

摘要： For a compact negatively curved space, we develop a notion of thermodynamic formalism and apply it to study the space of quasi-morphisms of its fundamental group modulo boundedness. We prove that this space is Banach isomorphic to the space of Bowen functions corresponding to the associated Gromov geodesic flow, modulo a weak notion of Livsic cohomology. The results include that each such unbounded quasi-morphism is associated with a unique invariant measure for the flow, and this measure uniquely characterizes the cohomology class. As a consequence, we establish the Central Limit Theorem for any unbounded quasi-morphism with respect to Markov measures, the invariance principle, and the Bernoulli property of the associated equilibrium state.