黄保军.(R)型准可解流形上映射同伦类的拓扑熵的下确界[J].数学研究及应用,2021,41(3):291~302 |
(R)型准可解流形上映射同伦类的拓扑熵的下确界 |
Infimum of Topological Entropies of Homotopy Classes of Maps on Infra-solvmanifolds of Type (R) |
投稿时间:2020-04-29 修订日期:2020-11-13 |
DOI:10.3770/j.issn:2095-2651.2021.03.007 |
中文关键词: 下确界 拓扑熵 同论 (R)型准可解流形 |
英文关键词:infimum topological entropy homotopy infra-solvmanifolds of type (R) |
基金项目:亳州市高层次人才引进基金项目, 安徽省自然科学基金(Grant No.KJ2019A1300). |
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中文摘要: |
设$f$是(R)型准可解流形$M$上的连续自映射, $N^\infty(f)$是$f$的渐近Nielsen数,本文将利用Nielsen不动点理论,给出$\log\,N^\infty(f)$是$f$的映射同伦类的拓扑熵的下确界的充分条件,这些条件将推广准幂零流形上的类似结果. |
英文摘要: |
Let $f$ be a continuous map on infra-solvmanifold $M$ of type (R) and $N^{\infty}(f)$ be the asymptotic Nielsen number of $f$. In this paper, the sufficient conditions to assure that $\log N^{\infty}(f)$ is the infimum of topological entropies of the homotopy class of the map $f$ are given by using Nielsen fixed point theory. These conclusions will generalize the similar results on infra-nilmanifolds. |
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