标题： 准同态的热力学形式化：有界上同调与统计学 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化概念，并将其应用于研究基本群的拟同态模去有界性的空间。 我们证明了这个空间在弱Livsic上同调的意义下与对应Gromov测地流的Bowen函数空间Banach同构。 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，且该测度唯一确定了上同调类。 由此得出结论，我们建立了关于Markov测度下任意无界拟同态的中心极限定理、不变性原理以及与平衡态相关的Bernoulli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.