The sequence asymptotic average shadowing property and transitivity

Volume 9, Issue 6, pp 3600--3610 http://dx.doi.org/10.22436/jnsa.009.06.13

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Authors

Tao Wang - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China. Jiandong Yin - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China. Qi Yan - Department of Mathematics, Nanchang University, Nanchang 330031, P. R. China.

Abstract

Let \(X\) be a compact metric space and \(f\) be a continuous map from \(X\) into itself. In this paper, we introduce the concept of the sequence asymptotic average shadowing property, which is a generalization of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence asymptotic average shadowing property and investigate the relationship between the sequence asymptotic average shadowing property and transitivity.

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Keywords

• Sequence asymptotic average shadowing property
• chain transitive
• weakly almost periodic point
• transitivity
• weakly mixing.

MSC

•  34D05
•  37D45

References

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