Minimal set of periods for continuous self-maps of the eight space

Fixexd point theory and applications

article

Llibre, Jaume¹  Sá, Ana² 

[1] Universitat Autònoma de Barcelona;Departamento de Matemática, Universidade Nova de Lisboa

关键词: Continuous maps;    Periodic orbit;    Period;    Minimal period;    The space in shape of eight;   

DOI  :  10.1186/s13663-020-00687-9

来源: SpringerOpen

【 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.

【 授权许可】

Unknown