关于映射同伦类的拓扑熵

On the Topological Entropy of Homotopy Class for Maps

设ｆ：Ｔｍ→Ｔｍ为ｍ维环面自映射，Ｎ∞（ｆ）是ｆ的渐近Ｎｉｅｌｓｅｎ数，本文应用Ｎｉｅｌｓｅｎ不动点理论，给出了ｌｏｇＮ∞（ｆ）是ｆ的同伦类的拓扑熵的最好下界的一个充要条件；并通过在齐性空间上引入等价度量。

Let f: T m→ T m be a continuous selfmap of m dimensional torus, N ∞(f) be asymptotic Nielsen number of f, the paper gives a sufficient and necessary condition to assure that log N ∞(f) is best lower bound of topological entropy of homotopy class for f by using Nielsen fixed point theory, and extends it to case for the selfmaps of nilmanifolds by introducing equivalent metric on the homogeneous spaces.