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标题：Minimal set of periods for continuous self-maps of the eight space
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作者：Jaume Llibre ; Ana Sá
期刊名称：Fixed Point Theory and Applications
印刷版ISSN：1687-1820
电子版ISSN：1687-1812
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13663-020-00687-9
出版社：Hindawi Publishing Corporation
摘要：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.