On the limit quasi-shadowing property

Fang Zhang; Yunhua Zhou

doi:10.3934/dcds.2017123

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2017, Volume 37, Issue 5: 2861-2879. Doi: 10.3934/dcds.2017123

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On the limit quasi-shadowing property

Fang Zhang^1, and
Yunhua Zhou^2, ,

1.
Chongqing College of Humanities Science and Technology, Chongqing, 401524, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

* Corresponding author
* Corresponding author

Received: October 31, 2014

Revised: November 30, 2016

Published: May 2017

The second author is supported by NSFC (11471056) and Foundation and Frontier Research Program of Chongqing (cstc2016jcyjA0312).

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Abstract

In this paper, we study the limit quasi-shadowing property for diffeomorphisms. We prove that any quasi-partially hyperbolic pseudoorbit $\{x_{i},n_{i}\}_{i∈ \mathbb{Z}}$ can be $\mathcal{L}^p$-, limit and asymptotic quasi-shadowed by a points sequence $\{y_{k}\}_{k∈ \mathbb{Z}}$. We also investigate the $\mathcal{L}^p$-, limit and asymptotic quasi-shadowing properties for partially hyperbolic diffeomorphisms which are dynamically coherent.

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Mathematics Subject Classification: Primary: 37C50; Secondary: 37D30.

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References

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