Spectral sequences in Conley's theory

Autor(es)

Cornea, O. ^[1] ; de Rezende, K. A. ^[2] ; da Silveira, M. R. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7 - Canada

^[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Ergodic Theory and Dynamical Systems; v. 30, n. 4, p. 1009-1054, AUG 2010.
• Citações Web of Science: 8

Resumo

In this paper, we analyse the dynamics encoded in the spectral sequence (E(r), d(r)) associated with certain Conley theory connection maps in the presence of an `action' type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Delta to provide a system that spans E(r) in terms of the original basis of C and to identify all of the differentials d(p)(r) : E(p)(r) -> E(p-r)(r). In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E(p)(0) and E(p-r)(0)in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications. (AU)

• Processo FAPESP: 02/10246-2 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 03/13120-2 - Aplicações do Índice de Conley para variedades não-compactas
• Beneficiário: Mariana Rodrigues da Silveira
• Linha de fomento: Bolsas no Brasil - Doutorado