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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2008; 45(6): 1505-1521

Printed November 1, 2008

https://doi.org/10.4134/JKMS.2008.45.6.150

Copyright © The Korean Mathematical Society.

Structural stability of vector fields with orbital inverse shadowing

Keonhee Lee, Zoonhee Lee, and Yong Zhang

Chungnam National University, Chungnam National University, and Suzhou University

Abstract

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In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of $C^1$ vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].

Keywords: flow, method, orbital inverse shadowing, shadowing, structurally stable, vector field

MSC numbers: Primary 37C; Secondary 37D

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