VECTOR FIELDS WHOSE LINEARISATION IS HURWITZ ALMOST EVERYWHERE

Autor(es)

Pires, Benito ^[1] ; Rabanal, Roland ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Comp & Matemat, Fac Filosofia Ciencias & Letras, BR-14040901 Ribeirao Preto, SP - Brazil

^[2] Pontificia Univ Catolica Peru, Secc Matemat, Lima 32 - Peru

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 142, n. 9, p. 3117-3128, SEP 2014.
• Citações Web of Science: 2

Resumo

A real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided. Let X : R-2 -> R-2 be a C-1 vector field whose Jacobian matrix DX(p) is Hurwitz for Lebesgue almost all p is an element of R-2. Then the singularity set of X is either an empty set, a one-point set or a non-discrete set. Moreover, if X has a hyperbolic singularity, then X is topologically equivalent to the radial vector field (x, y) bar right arrow (-x, -y). This generalises BGAS to the case in which the vector field is not necessarily a local diffeomorphism. (AU)

• Processo FAPESP: 09/02380-0 - Fluxos em superfícies e transformações de intercâmbio
• Beneficiário: Benito Frazao Pires
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores
• Processo FAPESP: 08/02841-4 - Teoria topológica, geométrica e ergódica dos sistemas dinâmicos
• Beneficiário: Jorge Manuel Sotomayor Tello
• Modalidade de apoio: Auxílio à Pesquisa - Temático