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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.)


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Pires, Benito [1] ; Rabanal, Roland [2]
Total Authors: 2
[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

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