VECTOR FIELDS WHOSE LINEARISATION IS HURWITZ ALMOST EVERYWHERE

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 142, n. 9, p. 3117-3128, SEP 2014.
• Web of Science Citations: 2

Abstract

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)

• FAPESP's process: 09/02380-0 - Flows on surfaces and exchange transformations
• Grantee: Benito Frazao Pires
• Support Opportunities: Research Grants - Young Investigators Grants
• FAPESP's process: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems
• Grantee: Jorge Manuel Sotomayor Tello
• Support Opportunities: Research Projects - Thematic Grants