On the density of various shadowing properties
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 981-989
https://doi.org/10.4134/CKMS.c180290
Published online July 31, 2019
Namjip Koo, Nyamdavaa Tsegmid
Chungnam National University; Mongolian National University of Education
Abstract : In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f : X \to X$ be a continuous map of a compact metric space $X$ and $A$ be an $f$-invariant dense subspace of $X$. We show that if $f|_A:A\to A$ has the periodic shadowing property, then $f$ has the periodic shadowing property. Also, we show that $f$ has the finite average shadowing property if and only if $f|_A$ has the finite average shadowing property.
Keywords : periodic shadowing, finite average shadowing, invariant dense subset
MSC numbers : Primary 37C50, 54H20, 37B99
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