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Structural stability of vector fields with orbital inverse shadowing

이준희|Yong Zhang|이건희
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회지 (Journal of the KMS)|제45권 제6호|pp. 1505-1521

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참고문헌

키워드

shadowingmethodflowvector fieldorbital inverse shadowingstructurally stable
주제분류수학

초록

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 C¹ interior of the set of C¹ 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].

Abstract

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 C¹ interior of the set of C¹ 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].

참고문헌 (26)

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관련 논문AI추천

ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C¹ VECTOR FIELDS이건희, Le Huy Tien, Xiao Wen대한수학회 · 대한수학회지2014 · 제51권 제1호Hyperbolicity of chain transitive sets with limit shadowing이승희, Abbas Fakhari, Khosro Tajbakhsh대한수학회 · 대한수학회보2014 · 제51권 제5호Shadowing, expansiveness and stability of divergence-free vector fieldsCelia Ferreira대한수학회 · 대한수학회보2014 · 제51권 제1호Shadowable chain components and hyperbolicity박준미, 이만섭, 이승희대한수학회 · 대한수학회보2015 · 제52권 제1호C^1-stable inverse shadowing chain components for generic diffeomorphismsManseob Lee대한수학회 · 대한수학회논문집2009 · 제24권 제1호Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems이만섭대한수학회 · 대한수학회지2021 · 제58권 제5호

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