一种点熵的估计与计算

对紧度量空间X上的连续自映射f：X→X，Hurley利用一点逆像的(n，ε)，分离子集，引入了熵hp(f)和hm(f)。按照拓扑熵观点，它们也度量了系统(X，f)的复杂性，本文将以Nielsen根类理论为工具，首先给出hp(f)的一个恰当的下界估计；然后作为该结果的应用，我们具体计算了环面上一类自映射的熵hp(f)，同时得到了该空间上自映射同伦类熵的一个下界估计。

Estimation and Computation of a Kind of Point Entropy

Let X be a compact metric space and f: X → X a continuous map, the entropy hm(f) and hp(f), which were defined by Hurley in terms of (n, ε)-separated subsets of inverse images of individual points, measure complexity of the system(X, f) in topological entropy point of view. In this paper, we give firstly the estimation of lower bound of hp(f)by using Nielsen root class theory. Secondly, as the applications of the result, we compute the entropies hp(f) of typical selfmaps on tori, as well as obtaining a lower bound of the entropies of homotopy class for the selfmaps on these spaces.