- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2013
2
Chain recurrence in $\beta $-compactifications of topological groups
Josiney
Souza
Universidade Estadual de Maringá, MARINGÁ, PR, BRAZIL
Transformation group, attractor, Morse decomposition, chain recurrence, Stone–Čech compactification
Let $G$ be a topological group. In this paper limit behavior in the Stone–Čech compactification $\beta G$ 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 $% \beta G$ 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 $\beta G$. Applications of chain recurrent function to linear differential systems and transformation groups are done.
Dynamical systems and ergodic theory
General
475
493
10.4171/GGD/191
http://www.ems-ph.org/doi/10.4171/GGD/191