α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR

doi:10.1007/s10473-022-0225-6

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 813-824.doi: 10.1007/s10473-022-0225-6

• 论文 • 上一篇

α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR

丁义明, 孙运

Center for Mathematical Sciences, School of Science, Wuhan University of Technology, Wuhan 430070, China

收稿日期:2020-12-28 修回日期:2021-05-12 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Yiming DING,E-mail:dingym@whut.edu.cn E-mail:dingym@whut.edu.cn
作者简介:Yun SUN,E-mail:sunyun@whut.edu.cn
基金资助:
This work was supported by the National Key Research and Development Program of China (2020YFA0714200), and also supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology (2018-YS-077).

α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR

Yiming DING, Yun SUN

Center for Mathematical Sciences, School of Science, Wuhan University of Technology, Wuhan 430070, China

Received:2020-12-28 Revised:2021-05-12 Online:2022-04-25 Published:2022-04-22
Supported by:
This work was supported by the National Key Research and Development Program of China (2020YFA0714200), and also supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology (2018-YS-077).

摘要/Abstract

摘要： We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals and so on. Under the finiteness and basin conditions, we provide a leveled A-R pair decomposition for such maps, and characterize α-limit set of each point. Based on weak Morse decomposition of X, we construct a bounded Lyapunov function V (x), which gives a clear description of orbit behavior of each point in X except a meager set.

关键词: Attracting set, leveled A-R pair decomposition, α-limit set, Lyapunov function

Abstract: We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X. This kind of map is a generalization of maps such as topologically expansive Lorenz map, unimodal map without homtervals and so on. Under the finiteness and basin conditions, we provide a leveled A-R pair decomposition for such maps, and characterize α-limit set of each point. Based on weak Morse decomposition of X, we construct a bounded Lyapunov function V (x), which gives a clear description of orbit behavior of each point in X except a meager set.

Key words: Attracting set, leveled A-R pair decomposition, α-limit set, Lyapunov function

中图分类号:

37B25

丁义明, 孙运. α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR[J]. 数学物理学报(英文版), 2022, 42(2): 813-824.

Yiming DING, Yun SUN. α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR[J]. Acta mathematica scientia,Series B, 2022, 42(2): 813-824.

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α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR

α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR

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