Flows with the weak two-sided limit shadowing property

Jihoon Lee; Ngocthach Nguyen

doi:10.3934/dcds.2021040

Article Contents

2021, Volume 41, Issue 9: 4375-4395. Doi: 10.3934/dcds.2021040

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Flows with the weak two-sided limit shadowing property

Jihoon Lee^1, and
Ngocthach Nguyen^2, ,

1.
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
2.
Department of Mathematics, Chungnam National University, Daejeon 34134, Korea

^* Corresponding author: Ngocthach Nguyen
^* Corresponding author: Ngocthach Nguyen

Received: March 31, 2020

Revised: July 31, 2020

Early access: March 2021

Published: September 2021

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Abstract

In this paper we study the weak two-sided limit shadowing for flows on a compact metric space which is different with the usual shadowing, two-sided limit shadowing and L-shadowing, and characterize the weak two-sided limit shadowing flows from the pointwise and measurable viewpoints. Moreover, we prove that if a flow $ \phi $ has the weak two-sided limit shadowing property on its chain recurrent $ CR(\phi) $ then the set $ CR(\phi) $ is decomposed by a finite number of closed invariant sets on which $ \phi $ is topologically transitive and has the two-sided limit shadowing property.

Keywords:

Expansiveness,
shadowing property,
spectral decomposition,
transitivity,
weak two-sided limit shadowing property.

Mathematics Subject Classification: Primary: 37B99; Secondary: 37D99.

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References

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