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| Author(s): |
Adriano João da Silva
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2010-03-26 |
| Examining board members: |
Luiz Antonio Barrera San Martin;
Alexandre José Santana;
Pedro Jose Catuogno
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| Advisor: | Luiz Antonio Barrera San Martin |
| Abstract | |
Let G be a connected semi-simple Lie group with finite center and S C G a semigroup with interior points. Let G/L be a homogeneous space. There is a natural action of S on G/L. The relation x =y se y e Sx, x, y e G/L, is transitive but not reflexive nor symmetric. Roughly, a control set is a subset D C G/L, inside of which reflexivity and simmetry for _ hold. Control sets are studied in G=L when L is a parabolic subgroup. They are characterized by means of the Weyl chambers in G meeting intS. Thus, for each ? e W, the Weyl group of G, there is a control set D? D1 is the only invariant control set, and the subset W(S) = {?; D? = D1} turns out to be a subgroup. The1 control sets in the maximal flag are determined by W(S) nW (AU) | |
| FAPESP's process: | 07/06865-2 - Lie Groups and Control Systems |
| Grantee: | Adriano João da Silva |
| Support Opportunities: | Scholarships in Brazil - Master |