Xianjuan Liang | Searcharxiv

arXiv2026

Return time sets and product recurrence

Let $G$ be a countable infinite discrete group. We show that a subset $F$ of $G$ contains a return time set of some piecewise syndetic recurrent point $x$ in a compact Hausdorff space $X$ with a $G$-action if and only if $F$ is a quasi-central set. As an application, we show that if a nonempty closed subsemigroup $S$ of the Stone-Čech compactification $βG$ contains the smallest ideal $K(βG)$ of $βG$ then $S$-product recurrent is equivalent to distality, which partially answers a question of Auslander and Furstenberg (Trans. Amer. Math. Soc. 343, 1994, 221--232).

math.DS↗

arXiv2021

Graph maps with zero topological entropy and sequence entropy pairs

We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal $ω$-limit set), and a non-diagonal pair is an NS-pair if and only if it is an IN-pair if and only if it is an IT-pair. This completes characterization of zero topological sequence entropy for graph maps.

math.DS↗