A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS*

doi:10.1007/s10473-023-0115-6

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 259-288.doi: 10.1007/s10473-023-0115-6

A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*

Bo Han^1,†, Manseob Lee²

1. LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing 100191, China;
2. Department of Marketing Big Data and Mathematics, Mokwon University, Daejeon 35349, Korea

收稿日期:2021-06-01 修回日期:2022-06-21 发布日期:2023-03-01
通讯作者: † Bo HAN.E-mail: hanbo@buaa.edu.cn
基金资助:
*National Natural Science Foundation of China (12071018) and Fundamental Research Funds for the Central Universities, and the second author was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MIST) (2020R1F1A1A01051370).

A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*

Bo Han^1,†, Manseob Lee²

1. LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing 100191, China;
2. Department of Marketing Big Data and Mathematics, Mokwon University, Daejeon 35349, Korea

Received:2021-06-01 Revised:2022-06-21 Published:2023-03-01
Contact: † Bo HAN.E-mail: hanbo@buaa.edu.cn
About author:Manseob Lee,E-mail: lmsds@mokwon.ac.kr
Supported by:
*National Natural Science Foundation of China (12071018) and Fundamental Research Funds for the Central Universities, and the second author was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MIST) (2020R1F1A1A01051370).

摘要/Abstract

摘要： In this paper, we define a generalized Lipschitz shadowing property for flows and prove that a flow $\phi$ generated by a $C^1$ vector field $X$ on a closed Riemannian manifold $M$ has this generalized Lipschitz shadowing property if and only if it is structurally stable.

关键词: flow, Perron property, hyperbolicity, generalized Lipschitz shadowing property, structural stability

Abstract: In this paper, we define a generalized Lipschitz shadowing property for flows and prove that a flow $\phi$ generated by a $C^1$ vector field $X$ on a closed Riemannian manifold $M$ has this generalized Lipschitz shadowing property if and only if it is structurally stable.

Key words: flow, Perron property, hyperbolicity, generalized Lipschitz shadowing property, structural stability

Bo Han, Manseob Lee. A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*[J]. 数学物理学报(英文版), 2023, 43(1): 259-288.

Bo Han, Manseob Lee. A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 259-288.

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A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*

A GENERALIZED LIPSCHITZ SHADOWING PROPERTY FOR FLOWS^*

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