标题： 关于球体扩张映射 显示英文标题

标题： On ball expanding maps

摘要： 我们研究球扩张映射的动力学性质，这是一类定义在紧致度量空间上的连续自映射。 对于一个球扩张映射，我们证明了以下结论：(1) 周期点的集合在链回归集中是稠密的；(2) 如果映射的拓扑熵为零，则链回归集是有限的；(3) 映射只有有限多个链成分；(4) 如果空间是完美的，则映射的拓扑熵是正的；(5) 如果空间是连通的，则映射是局部最终满射的，因此是混合的。 还提供了几个例子。 显示英文摘要

摘要： We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if the topological entropy of the map is zero, then the chain recurrent set is finite; (3) the map has only finitely many chain components; (4) if the space is perfect, then the topological entropy of the map is positive; and (5) if the space is connected, then the map is locally eventually onto and hence mixing. Several examples are also provided.