TY - JOUR
T1 - Minimal set of periods for continuous self-maps of the eight space
AU - Llibre, Jaume
AU - Sá, Ana
N1 -
MTM2016-77278-P
grant 2017SGR1617
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
SN - 1687-1820
VL - 2021
JO - Fixed Point Theory and Algorithms for Sciences and Engineering
JF - Fixed Point Theory and Algorithms for Sciences and Engineering
IS - 1
M1 - 3
ER -