连续自映射的拓扑r-熵及其性质

Topological r-entropy of a continuous self-mapping and its properties

针对紧致度量空间上的连续自映射,本文给出了拓扑熵的一种新的定义,并讨论了这种拓扑熵的一些重要性质。证明了该拓扑熵与度量的选取无关,是拓扑共轭不变量,该拓扑熵对迭代系统具有可加性。同时,就系统在非游荡点集上的限制的这种拓扑熵与原系统的熵之间的关系进行了讨论,得到二者之间的一个不等式关系。

This paper introduces a new concept of topological entropy of a continuous elf-mapping on a compact metric space, and discusses some inportant properties of it. The following results are proved. The new topological entropy is independent of the choice of the metric and it is an invariant of topological conjugacy; the new topological entropy is addable for the iterations of the system. Meanwhile, the paper discusses the relationship between the new topological entropy of the retriction on the non-wandering set and that of the original system, and an inequality is acquired.