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

^*Corresponding author for this work

School of Artificial Intelligence(Institute of Artificial Intelligence)

Zhongguancun Laboratory
Liaoning University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	403-427
Number of pages	25
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	54
DOIs	https://doi.org/10.3934/dcds.2026071
State	Published - 30 Mar 2026

Keywords

Hyperbolicity
expansiveness
shadowing property

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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",

year = "2026",

month = mar,

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doi = "10.3934/dcds.2026071",

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

AU - Wen, Xiao

AU - Yang, Yinong

PY - 2026/3/30

Y1 - 2026/3/30

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

EP - 427

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

Abstract

Keywords

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