Topological invariants for singularities of real vector fields in dimension three

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October 2008, 20(4): 823-847. doi: 10.3934/dcds.2008.20.823

Topological invariants for singularities of real vector fields in dimension three

C. Alonso-González ^1, , M. I. Camacho ^2, and F. Cano ^3,

1.	Dpto. de Estadística e Investigación Operativa, Universidad de Alicante, 03690 San Vicente del Raspeig, Alicante, Spain
2.	Foundation Getulio Vargas, Rio de Janeiro, Brazil
3.	Dpto. Álgebra, Geometría y Topología, Universidad de Valladolid, 47005 Valladolid, Spain

Received December 2006 Revised September 2007 Published January 2008

Abstract
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We give topological invariants for a wide class of abso-lutely isolated singularities of three-dimensional real vector fields. Our invariants are complete once the desingularization morphism $\pi$ is fixed. They are obtained in terms of a finite set of configurations depending only on the eigenvalues of the singularities.

Keywords: Qualitative theory, blowing-ups, singularities, saddle-connections., topological classification, vector fields.

Mathematics Subject Classification: Primary: 34C081.

Citation: C. Alonso-González, M. I. Camacho, F. Cano. Topological invariants for singularities of real vector fields in dimension three. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 823-847. doi: 10.3934/dcds.2008.20.823

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