标题： 非一致系统带有受控规范性和熵膨胀性的热力学形式主义 显示英文标题

标题： Thermodynamic formalism for non-uniform systems with controlled specification and entropy expansiveness

摘要： 我们研究了具有非一致结构的动力系统的热力学形式论。具体来说，通过推广 Climenhaga-Thompson 的轨道分解准则，我们得到了一族非一致扩张流的平衡态的唯一性。特别地，这一族包括熵扩张流。同时，分解中的关键部分允许满足一个甚至更弱版本的规范性，即受控规范性，从而扩展了 Pavlov 相应的结果。我们探讨了这两个抽象定理的两个应用。首先，我们引入了一个称为弱 Walters 条件的正则性条件，并研究了满足该条件的屋顶函数的吊射流的最大熵测度的唯一性。其次，我们研究了秩一非正曲率流形上的拓扑传递框架流，这是非一致双曲流的群扩张。在满足某一束曲率条件并运行高斯-博内型论证的情况下，我们证明了某些势函数的平衡态的唯一性。 显示英文摘要

摘要： We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit decomposition criteria. In particular, such family includes entropy expansive flows. Meanwhile, the essential part of the decomposition is allowed to satisfy an even weaker version of specification, namely controlled specification, thus also extends the corresponding results by Pavlov. Two applications of our abstract theorems are explored. Firstly, we introduce a notion of regularity condition called weak Walters condition, and study the uniqueness of measure of maximal entropy for a suspension flow with roof function satisfying such condition. Secondly, we investigate topologically transitive frame flows on rank one manifolds of nonpositive curvature, which is a group extension of nonuniformly hyperbolic flows. Under a bunched curvature condition and running a Gauss-Bonnet type of argument, we show the uniqueness of equilibrium states with respect to certain potentials.