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

Jaume Llibre, Ana Sá

Research output: Contribution to journalArticlepeer-review

Abstract

Let Gk 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 Gk. Thus, G1 is the circle, G2 is the eight space, and G3 is the trefoil. Let f: Gk→ Gk be a continuous map such that, for k> 1 , the branching point is fixed. If Per (f) denotes the set of periods of f, the minimal set of periods of f, denoted by MPer (f) , is defined as ⋂ gfPer (g) where g: Gk→ Gk is homological to f. The sets MPer (f) are well known for circle maps. Here, we classify all the sets MPer (f) for self-maps of the eight space.

Original languageEnglish
Article number3
JournalFixed Point Theory and Algorithms for Sciences and Engineering
Volume2021
Issue number1
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Continuous maps
  • Minimal period
  • Period
  • Periodic orbit
  • The space in shape of eight

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