Positively expansive maps and the limit shadowing properties
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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.
Abstract
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.
참고문헌 (15)
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