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On Periodic Shadowing Property

Journal: Sahand Communications in Mathematical Analysis (Vol.14, No. 1)

Publication Date:

Authors : ;

Page : 63-72

Keywords : Periodic shadowing; Shadowing; Chain transitive; Distal;

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In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chaotic in the sense of Li-Yorke. Moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.

Last modified: 2019-04-28 14:13:45