摘要
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.
出处
《数学进展》
CSCD
北大核心
1997年第3期241-244,共4页
Advances in Mathematics(China)
基金
煤炭青年科研基金
关键词
拓扑熵
同伦类
幂零流形
映射
动力系统
topological entropy
homotopy class
asymptotic Nielsen number
nilmanifolds