Oriented and orbital shadowing for vector fields-Reference-Cited by-同舟云学术

Oriented and orbital shadowing for vector fields

Published:2022 Issue:10 Volume:42 Page:5087
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Li Ming¹,Liu Xingzhong²

Affiliation:

1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

2. School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Abstract

<p style='text-indent:20px;'>In this paper, we prove that the <inline-formula><tex-math id="M1">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula>-interior of the set of vector fields having the oriented shadowing property coincides with the <inline-formula><tex-math id="M2">\begin{document}$ C^1 $\end{document}</tex-math></inline-formula>-interior of the set of vector fields having the orbital shadowing property.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference19 articles.

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3. S. Gan, M. Li.Orbital shadowing for $3$-flows, J. Differ. Equ., 262 (2017), 5022-5051.

4. S. Gan, M. Li, S. B. Tikhomirov.Oriented shadowing property and $\Omega$-stability for vector fields, J. Dyn. Differ. Equ., 28 (2016), 225-237.

5. K. Lee, K. Sakai.Structural stability of vector fields with shadowing, J. Differ. Equ., 232 (2007), 303-313.