论文标题
关于零维局部紧凑流的复发，并以紧凑的相组组成
On recurrence in zero-dimensional locally compact flow with compactly generated phase group
论文作者
论文摘要
令$ x $为零维当地紧凑的Hausdorff空间，不一定是公制，而$ g $是紧凑的拓扑组不一定是Abelian或可数。 We define recurrence at a point for any continuous action of $G$ on $X$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i) this dynamics is pointwise recurrent, (ii) $X$ is a union of $G$-minimal sets, (iii) the $G$-orbit closure relation is closed in $X\times X$, and （iv）$ x \ ni x \ mapsto \ edimine {gx} \ in 2^x $是连续的，是成对等效的。因此，如果这种动态是远端，则是等效的。
Let $X$ be a zero-dimensional locally compact Hausdorff space not necessarily metric and $G$ a compactly generated topological group not necessarily abelian or countable. We define recurrence at a point for any continuous action of $G$ on $X$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i) this dynamics is pointwise recurrent, (ii) $X$ is a union of $G$-minimal sets, (iii) the $G$-orbit closure relation is closed in $X\times X$, and (iv) $X\ni x\mapsto \overline{Gx}\in 2^X$ is continuous, are pairwise equivalent. Consequently, if this dynamics is distal, then it is equicontinuous.
