Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 22 (2012), No. 4, 931--948Copyright Heldermann Verlag 2012 Semigroup Actions on Adjoint Orbits Osvaldo G. do Rocio Dep. de Matemática, Universidade Estadual de Maringá, UEM, Avenida Colombo 5790, 87020-900 - Maringá - PR, Brazil rocio@uem.br Luiz A. B. San Martin Dep. de Matemática, Universidade Estadual de Campinas, UNICAMP, Cx. Postal 6065, 13.083-859 - Campinas - SP, Brazil smartin@ime.unicamp.br Marcos André Verdi Dep. de Matemática, Universidade Estadual de Maringá, UEM, Avenida Colombo 5790, 87020-900 - Maringá - PR, Brazil maverdi@uem.br [Abstract-pdf] Let $G$ be a connected semi-simple Lie group with finite center and $S\subset G$ a subsemigroup with ${\rm int}\, S\neq \emptyset$. In this article we study the control sets for the actions of $S$ on the adjoint orbits ${\rm Ad}(G)H$, where $H$ is a regular element in the Lie algebra of $G$. We show here that these sets can be described as sets of fixed points for regular elements in the interior of $S$. Moreover, we shall describe the domains of attraction of this control sets and show that these sets are not comparable with respect to the natural order on control sets. Keywords: Semigroup, adjoint orbits, regular elements. MSC: 22F30 [ Fulltext-pdf  (314  KB)] for subscribers only.