Minimal set of periods for continuous self-maps of the eight space
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Sá, Ana (Universidade Nova de Lisboa. Departamento de Matemática (Portugal))

Date:	2021
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 ⋂g≃fPer(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.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017SGR1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Continuous maps ; Periodic orbit ; Period ; Minimal period ; The space in shape of eight
Published in:	Fixed Point Theory and Algorithms for Sciences and Engineering, Vol. 2021, Issue 1 (December 2021) , art. 3, ISSN 2730-5422

DOI: 10.1186/s13663-020-00687-9

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