JORDAN DECOMPOSITION AND DYNAMICS ON FLAG MANIFOLDS

Autor(es)

Ferraiol, Thiago ^[1] ; Patrao, Mauro ^[2] ; Seco, Lucas ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

^[2] Univ Brasilia, Dept Matemat, BR-70904970 Brasilia, DF - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 26, n. 3, p. 923-947, MAR 2010.
• Citações Web of Science: 8

Resumo

Let g be a real semisimple Lie algebra and G = Int(g). In this article, we relate the Jordan decomposition of X is an element of g (or g is an element of G) with the dynamics induced on generalized flag manifolds by the right invariant continuous-time flow generated by X (or the discrete-time flow generated by g). We characterize the recurrent set and the finest Morse decomposition (including its stable sets) of these flows and show that its entropy always vanishes. We characterize the structurally stable ones and compute the Conley index of the attractor Morse component. When the nilpotent part of X is trivial, we compute the Conley indexes of all Morse components. Finally, we consider the dynamical aspects of linear differential equations with periodic coefficients in g, which can be regarded as an extension of the dynamics generated by an element X is an element of g. In this context, we generalize Floquet theory and extend our previous results to this case. (AU)

• Processo FAPESP: 07/07610-8 - Ações de grupos e sistemas dinâmicos em fibrados
• Beneficiário: Thiago Fanelli Ferraiol
• Modalidade de apoio: Bolsas no Brasil - Doutorado