Let be a topological group. In this paper limit behavior in the Stone–Čech compactification is studied. It depends on a family of translates of a reversible subsemigroup . 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 whenever 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 . Applications of chain recurrent function to linear differential systems and transformation groups are done.
Cite this article
Josiney A. Souza, Chain recurrence in -compactifications of topological groups. Groups Geom. Dyn. 7 (2013), no. 2, pp. 475–493DOI 10.4171/GGD/191