No-shadowing for singular hyperbolic sets with a singularity

Xiao Wen; Lan Wen

doi:10.3934/dcds.2020258

No-shadowing for singular hyperbolic sets with a singularity

Xiao Wen
, Lan Wen

人工智能学院(人工智能研究院)

Peking University

科研成果: 期刊稿件 › 文章 › 同行评审

11 引用（Scopus）

摘要

We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star ow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.

源语言	英语
页（从-至）	6043-6059
页数	17
期刊	Discrete and Continuous Dynamical Systems- Series A
卷	40
期	10
DOI	https://doi.org/10.3934/dcds.2020258
出版状态	已出版 - 10月 2020

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AB - We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star ow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.

KW - Multisingular hyperbolicity

KW - Shadowing property

KW - Singular hyperbolicity

KW - Star flows

UR - https://www.scopus.com/pages/publications/85087956326

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DO - 10.3934/dcds.2020258

M3 - 文章

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No-shadowing for singular hyperbolic sets with a singularity

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