| (R)型准可解流形上映射同伦类的拓扑熵的下确界 |
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| 引用本文： | 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. |
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| 作者姓名： | 黄保军 |
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| 作者单位： | 亳州学院电子与信息工程系, 安徽 亳州 236800; 淮北师范大学数学科学学院, 安徽 淮北 235000 |
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| 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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| 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.
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| 关 键 词： | 下确界 拓扑熵 同论 (R)型准可解流形 |
| 收稿时间： | 2020/4/29 0:00:00 |
| 修稿时间： | 2020/11/13 0:00:00 |
Infimum of Topological Entropies of Homotopy Classes of Maps on Infra-solvmanifolds of Type (R) |
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| Baojun HUANG.Infimum of Topological Entropies of Homotopy Classes of Maps on Infra-solvmanifolds of Type (R)[J].Journal of Mathematical Research with Applications,2021,41(3):291-302. |
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| Authors: | Baojun HUANG |
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| Institution: | Department of Electronic and Information Engineering, Bozhou University, Anhui 236800, P. R. China; School of Mathematical Science, Huaibei Normal University, Anhui 235000, P. R. China |
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| Abstract: | 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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| Keywords: | infimum topological entropy homotopy infra-solvmanifolds of type (R) |
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