SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C1 VECTOR FIELDS

Xiao Wen; Yinong Yang

doi:10.3934/dcds.2026071

SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C¹ VECTOR FIELDS

Xiao Wen^*
, Yinong Yang

^*此作品的通讯作者

人工智能学院(人工智能研究院)

Zhongguancun Laboratory
Liaoning University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We prove that a generic continuously differentiable vector field is star on a dynamically isolated transitive set, denoted as Λ, if and only if it has the shadowing property (respectively, is expansive) on every nonsingular compact invariant subset of Λ. Additionally, some brief applications of this result are presented.

源语言	英语
页（从-至）	403-427
页数	25
期刊	Discrete and Continuous Dynamical Systems- Series A
卷	54
DOI	https://doi.org/10.3934/dcds.2026071
出版状态	已出版 - 30 3月 2026

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10.3934/dcds.2026071

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title = "SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C1 VECTOR FIELDS",

abstract = "We prove that a generic continuously differentiable vector field is star on a dynamically isolated transitive set, denoted as Λ, if and only if it has the shadowing property (respectively, is expansive) on every nonsingular compact invariant subset of Λ. Additionally, some brief applications of this result are presented.",

keywords = "Hyperbolicity, expansiveness, shadowing property",

author = "Xiao Wen and Yinong Yang",

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T1 - SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C1 VECTOR FIELDS

AU - Wen, Xiao

AU - Yang, Yinong

PY - 2026/3/30

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N2 - We prove that a generic continuously differentiable vector field is star on a dynamically isolated transitive set, denoted as Λ, if and only if it has the shadowing property (respectively, is expansive) on every nonsingular compact invariant subset of Λ. Additionally, some brief applications of this result are presented.

AB - We prove that a generic continuously differentiable vector field is star on a dynamically isolated transitive set, denoted as Λ, if and only if it has the shadowing property (respectively, is expansive) on every nonsingular compact invariant subset of Λ. Additionally, some brief applications of this result are presented.

KW - Hyperbolicity

KW - expansiveness

KW - shadowing property

UR - https://www.scopus.com/pages/publications/105042310022

U2 - 10.3934/dcds.2026071

DO - 10.3934/dcds.2026071

M3 - 文章

AN - SCOPUS:105042310022

SN - 1078-0947

VL - 54

SP - 403

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

ER -

SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C1 VECTOR FIELDS

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SHADOWING, EXPANSIVITY, AND DYNAMIC ISOLATION FOR C¹ VECTOR FIELDS