We review some recent results on a class of maps, called Bowen – Series-like maps, obtained from a class of group presentations for surface groups. These maps are piecewise homeomorphisms of the circle with finitely many discontinuities. The topological entropy of each map in the class and its relationship with the growth function of the group presentation is discussed, as well as the computation of these invariants.

中文翻译：

---

论 Bowen 族——曲面群的类系列映射

我们回顾了一类地图的一些最新结果，称为 Bowen – 类系列地图，从一类表面组的组演示中获得。这些映射是具有有限多个不连续点的圆的分段同胚。讨论了类中每个映射的拓扑熵及其与群表示的增长函数的关系，以及这些不变量的计算。