环面上自映射的点态原像熵的可加性

The Additivity of Pointwise Preimage Entropy for Selfmaps on Torus

与拓扑熵一样,紧度量空间上连续自映射的点态原像熵(pointwise preimage entropy),是动力系统的不变量,但它的性质并不与其完全一致,例如映射笛卡尔积的点态原像熵的可加性等.本文给出环面上连续自映射满足笛卡尔积的点态原像熵的可加性的条件,并借此计算环面上一类连续自映射的点态原像熵.

Pointwise preimage entropy is similar to topological entropy but, in generM, their properties are not completely coincident such as additivity under Cartesian product. In this paper, we firstly give the conditions to the pointwise preimage entropy of the maps on tori satisfing additivity under Cartesian product. Then we will compute the pointwise preimage entropies of a kind of maps on tori.