关于熵的可交换性

不管在测度空间还是拓扑空间上,两个连续映射复合后,其熵与复合的先后次序有关,但满足一定条件后,有些复合的顺序是可以交换的,即交换秩序后的熵保持不变.详细回顾了一些关于熵的定义,讨论了两个映射复合后其测度熵、测度序列熵、拓扑熵、拓扑序列熵、二维映射的拓扑熵、旋转熵及拓扑压的可交换性.

On the Commutativity of Entropy

Regardless of a measurement space or a topological space, after two consecutive mappings composite, their entropy is correlated to the composite order, however, when some conditions are met, some of composite orders can be exchanged but the entropy keeps constant after the orders are exchanged. This paper reviews in detail the definitions related to the entropy, and discusses the commutativity of the metric entropy after the composite of two mappings, metric sequence entropy, topological entropy, topological sequence entropy, topological entropy of two dimensional mapping, rotational entropy and topological pressure.