TY - JOUR

T1 - Minimal set of periods for continuous self-maps of the eight space

AU - Llibre, Jaume

AU - Sá, Ana

N1 - Funding Information:
The first author has been partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Continuous maps

KW - Minimal period

KW - Period

KW - Periodic orbit

KW - The space in shape of eight

UR - http://www.scopus.com/inward/record.url?scp=85117012150&partnerID=8YFLogxK

U2 - 10.1186/s13663-020-00687-9

DO - 10.1186/s13663-020-00687-9

M3 - Article

AN - SCOPUS:85117012150

VL - 2021

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

SN - 2730-5422

IS - 1

M1 - 3

ER -