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On the density of various shadowing properties

구남집|Nyamdavaa Tsegmid
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 981-989|DOI 10.4134/CKMS.c180290

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참고문헌

키워드

periodic shadowingfinite average shadowinginvariant dense subset
주제분류수학

초록

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.

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.

참고문헌 (22)

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