Vector fields whose linearisation is Hurwitz almost everywhere
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:ℝ2→ℝ2 be a C1 vector field whose Jacobian matrix DX(p) is Hurwitz for Lebesgue almost all p∈ℝ2. 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)↦(-x,-y). This generalises BGAS to the case in which the vector field is not necessarily a local diffeomorphism.
Autor(es):Pires, Benito;
Rabanal, Roland
Año: 2014
Título de la revista: Proceedings of the American Mathematical Society
Volumen: 142
Número: 9
Página inicial - Página final: 3117-3128
ISSN: 1088-6826(online) 0002-9939(print)
Url: http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2014-12035-1/