Journal of the
Korean Mathematical Society JKMS

In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let $f$ be a positively expansive open map of a compact metric space $X$. It is proved that if $f$ is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if $X$ is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

Keywords: Positively expansive map, shadowing, limit shadowing, tow-sided limit shadowing, average shadowing, topologically transitive, topologically mixing

MSC numbers: Primary 37C50; Secondary 54H20, 37D20

Supported by: This work is supported by JSPS KAKENHI Grant Numbers 16K05167 and 19K03578