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On the number of control sets on projective spaces

1996; Elsevier BV; Volume: 29; Issue: 1 Linguagem: Inglês

10.1016/0167-6911(96)00047-3

1872-7956

Carlos J. Braga Barros, Luiz A. B. San Martín,

Geometric and Algebraic Topology

The purpose of this paper is to provide an upper bound for the number of control sets for linear semigroups acting on a projective space RPd−1. These semigroups and control sets were studied by Colonius and Kliemann (1993) who proved that there are at most d control sets. Here we apply the results of San Martin and Tonelli (1995) about control sets for semigroups in semisimple Lie groups and make a case by case analysis according to the transitive groups on RPd−1 which were classified by Boothby and Wilson (1975, 1979) in order to improve that upper bound. It turns out that in some cases there are at most d/2 or d/4 control sets.