The Conley index for discontinuous vector fields

Autor(es)

Casagrande, R. ^[1] ; de Rezende, K. A. ^[1] ; Teixeira, M. A. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, UNICAMP, Dept Math, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 136, n. 1, p. 47-56, OCT 2008.
• Citações Web of Science: 0

Resumo

In this paper, we define the Conley index h(D) for a region of discontinuity D of a piecewise C(k) discontinuous vector field Z on an n-dimensional compact Riemannian smooth orientable manifold and prove it to be a homotopy invariant. This invariance is obtained by regularization of the discontinuous vector field. We use an adapted form of Lyapunov graph continuation to produce, in a few examples, a regularization of the discontinuous vector field with the property that the dynamics in a regularized neighborhood of D has the same Conley index as h(D). (AU)

• Processo FAPESP: 02/10246-2 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 04/10229-6 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático