Otro
Controllability of control systems on complex simple lie groups and the topology of flag manifolds
Registro en:
Journal of Dynamical and Control Systems, v. 19, n. 2, p. 157-171, 2013.
1079-2724
3231282086023916
Autor
Santos, Ariane Luzia dos
Martin, Luiz Antonio Barreira San
Resumen
Let S be a subsemigroup with nonempty interior of a connected complex simple Lie group G. It is proved that S = G if S contains a subgroup G (α) ≈ Sl (2, C) generated by the exp g±α, where gα is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of S is contractible in some flag manifold if S is proper, and exploits the fact that several orbits of G (α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements. Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)