Let $G_{k}$ be a bouquet of circles, i.e., the quotient space of the interval $[0,k]$ obtained by identifying all points of integer coordinates to a single point, called the branching point of $G_{k}$ . Thus, $G_{1}$ is the circle, $G_{2}$ is the eight space, and $G_{3}$ is the trefoil. Let $f: G_{k} \to G_{k}$ be a continuous map such that, for $k>1$ , the branching point is fixed. If $\operatorname{Per}(f)$ denotes the set of periods of f, the minimal set of periods of f, denoted by $\operatorname{MPer}(f)$ , is defined as $\bigcap_{g\simeq f} \operatorname{Per}(g)$ where $g:G_{k}\to G_{k}$ is homological to f. The sets $\operatorname{MPer}(f)$ are well known for circle maps. Here, we classify all the sets $\operatorname{MPer}(f)$ for self-maps of the eight space.

中文翻译：

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八个空间的连续自映射的最小周期集

令$ G_ {k} $为一束圆，即通过将整数坐标的所有点标识为单个点（称为$ G_ {k的分支点）而获得的间隔$ [0，k] $的商空间} $。因此，$ G_ {1} $是圆，$ G_ {2} $是八个空格，$ G_ {3} $是三叶形。假设$ f：G_ {k} \ to G_ {k} $是一个连续映射，使得对于$ k> 1 $，分支点是固定的。如果$ \ operatorname {Per}（f）$表示f的周期集合，则用$ \ operatorname {MPer}（f）$表示的f的最小周期集合定义为$ \ bigcap_ {g \ simeq f} \ operatorname {Per}（g）$，其中$ g：G_ {k} \至G_ {k} $与f同源。集合$ \ operatorname {MPer}（f）$以圆图闻名。在此，我们将八个空间的自映射的所有集合$ \ operatorname {MPer}（f）$分类。