We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discussed by Bonk–Meyer and is closely related to coarse expanding conformal systems as defined by Haïssinsky–Pilgrim. We prove existence and uniqueness of equilibrium states for a wide class of potentials, as well as statistical laws such as a central limit theorem, law of iterated logarithm, exponential decay of correlations and a large deviation principle. Further, if the system is defined on the 2-sphere, we prove all such results even in presence of periodic (repelling) branch points.

我们考虑一类动力学系统，我们称其为弱粗扩展，它是对Bonk-Meyer讨论的扩展Thurston映射的临界后无限情况的推广，并且与Haïssinsky-Pilgrim定义的粗扩展共形系统密切相关。我们证明了广泛的势能平衡状态的存在性和唯一性，以及诸如中心极限定理，迭代对数律，相关性的指数衰减和大偏差原理之类的统计定律。此外，如果系统定义在2球面上，那么即使存在周期性（排斥）分支点，我们也可以证明所有此类结果。