Geodesic
Chain recurrence in $\beta $-compactifications of topological groups
Josiney A. Souza1
1Universidade Estadual de Maringá, Maringá, Brazil
Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 475-493

Voir la notice de l'article provenant de la source EMS Press

DOI

Let G be a topological group. In this paper limit behavior in the Stone–Čech compactification βG is studied. It depends on a family of translates of a reversible subsemigroup S. The notion of semitotal subsemigroup is introduced. It is shown that the semitotality property is equivalent to the existence of only two maximal chain transitive sets in βG whenever S is centric. This result links an algebraic property to a dynamical property. The concept of a chain recurrent function is also introduced and characterized via the compactification βG. Applications of chain recurrent function to linear differential systems and transformation groups are done.
DOI : 10.4171/ggd/191
Classification : 37-XX, 00-XX
Mots-clés : Transformation group, attractor, Morse decomposition, chain recurrence, Stone–Čech compactification

Josiney A. Souza  1

1 Universidade Estadual de Maringá, Maringá, Brazil 
Josiney A. Souza. Chain recurrence in $\beta $-compactifications of topological groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 475-493. doi: 10.4171/ggd/191
@article{10_4171_ggd_191,
     author = {Josiney A. Souza},
     title = {Chain recurrence in $\beta $-compactifications of topological groups},
     journal = {Groups, geometry, and dynamics},
     pages = {475--493},
     year = {2013},
     volume = {7},
     number = {2},
     doi = {10.4171/ggd/191},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/191/}
}
TY  - JOUR
AU  - Josiney A. Souza
TI  - Chain recurrence in $\beta $-compactifications of topological groups
JO  - Groups, geometry, and dynamics
PY  - 2013
SP  - 475
EP  - 493
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/191/
DO  - 10.4171/ggd/191
ID  - 10_4171_ggd_191
ER  - 
%0 Journal Article
%A Josiney A. Souza
%T Chain recurrence in $\beta $-compactifications of topological groups
%J Groups, geometry, and dynamics
%D 2013
%P 475-493
%V 7
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/191/
%R 10.4171/ggd/191
%F 10_4171_ggd_191

Cité par Sources :