论文标题
关于零dimsnions局部紧凑流的复发，并以紧凑的相组组成
On recurrence in zero-dimsnional locally compact flow with compactly generated phase group
论文作者
论文摘要
我们为紧凑型生成的Para-Tobological群体$ g $定义复发性，连续作用于本地紧凑的Hausdorff Space $ x $，$ \ dim x = 0 $，然后证明，如果$ \ overline {gx} $在x $中的所有$ x \ y Is $ x $ goint（i）$ x $ x $ x $ x $ x $ x $ compoint（i）集合，（iii）$ g $ -Orbit闭合关系以$ x \ times x $关闭，（iv）$ x \ ni x \ mapsto \ mapsto \ intline {gx} \ in 2^x $是连续的，是连续的，是成对的。因此，如果这种动力学反复出现，那么它几乎是周期性和等准的。此外，远端，紧凑和非连接的$ g $流具有非平凡的等效性，几乎是周期性的。
We define recurrence for a compactly generated para-topological group $G$ acting continuously on a locally compact Hausdorff space $X$ with $\dim X=0$, 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 pointwise product recurrent, then it is pointwise regularly almost periodic and equicontinuous; moreover, a distal, compact, and non-connected $G$-flow has a non-trivial equicontinuous pointwise regularly almost periodic factor.
