Communications of the
Korean Mathematical Society CKMS

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

Supported by: This work was supported by Basic Science Research Pro-gram through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2015R1D1A1A01060103).