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

School of Artificial Intelligence(Institute of Artificial Intelligence)

Peking University

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

11 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	6043-6059
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	40
Issue number	10
DOIs	https://doi.org/10.3934/dcds.2020258
State	Published - Oct 2020

Keywords

Multisingular hyperbolicity
Shadowing property
Singular hyperbolicity
Star flows

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10.3934/dcds.2020258

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title = "No-shadowing for singular hyperbolic sets with a singularity",

abstract = "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.",

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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

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DO - 10.3934/dcds.2020258

M3 - 文章

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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No-shadowing for singular hyperbolic sets with a singularity

Abstract

Keywords

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