幂零流形上自映射的点态原像熵的可加性

The Additivity of Pointwise Preimage Entropy for Selfmaps on Nilmanifolds

类似于拓扑熵,点态原像熵作为动力系统的不变量,也度量了紧度量空间上系统的复杂性.但至今不知其性质与拓扑熵是否完全一致,例如映射笛卡尔积的点态原像熵的可加性等.本文将把环面自映射笛卡尔积的点态原像熵的可加性,推广到紧幂零流形自映射的情形.

Pointwise preimage entropy is similar to topological entropy but,in general,their properties are not completely coincident such as additivity of under Cartesian product.In this paper we show that the description of the additivity of pointwise preimage entropy of the torus maps under Cartesian product given by myself extends to the case of the maps of compact nilmanifolds.