Non-dense orbit sets carry full metric mean dimension for maps with gluing orbit property

Abstract

In this paper, we analyze the non-dense orbit sets for maps with gluing orbit property. More precisely, let $f:X\to X$ be a continuous map with the gluing orbit property on a compact metric space $X$, in the setting, we show that for any non-transitive point $z_0\in X$, the set $E(z_0)$ is empty or carries full metric mean dimension.