关于拓扑熵下界的两点注记(英文)

Two Notes on Lower Bounds of Topological Entropy

英文关键词:topological entropy  asymptotic nielsen number  growth rate.

中文摘要:

      设ｆ：Ｘ→Ｘ是紧连通多面体自映射，应用Ｎｉｅｌｓｅｎ不动点理论，我们给出了ｆ的拓扑熵ｈ（ｆ）的一个更好下界。另外，若ｆ：Ｔ^m→T^m是ｍ－环面自映射，我们还得到了ｌｏｇＮ^∞（ｆ）是{h(g)|g≈f:T^m→T^m}的下确界的一个充要条件，这里Ｎ（ｆ）是ｆ的渐近Ｎｉｅｌｓｅｎ数，从而局部解答了姜伯驹教授提出的一个问题。

英文摘要:

      Let f:X→X be a selfmap of a compact connected polyhedron, using Nielsen fixed point theory, we give a better lower bound for topological entropy h(f) of f . In addition, if f:T^m→T^m is a selfmap of m-trous, some conditions under which log N^∞(f) is a best lower bound for {h(g)|g≈f:T^m→T^m} is obtained where N^∞(f ) is asymptotic Nielsen number of f, and hence we get the answer for a question put by Professor Boju Jiang.