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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

VECTOR FIELDS WHOSE LINEARISATION IS HURWITZ ALMOST EVERYWHERE

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Author(s):
Pires, Benito [1] ; Rabanal, Roland [2]
Total Authors: 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
Total Affiliations: 2
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: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems
Grantee:Jorge Manuel Sotomayor Tello
Support type: Research Projects - Thematic Grants
FAPESP's process: 09/02380-0 - Flows on surfaces and exchange transformations
Grantee:Benito Frazao Pires
Support type: Research Grants - Young Investigators Grants