A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES A tribute to Ivar Bendixson

Abstract : In this paper one extends results of Bendixson [B] and Dumortier [D] about the germs of vector fields with an isolated singularity at the origin of IR 2 , not accumulated by periodic orbits. As new tool, one introduces minimal curves, which are curves surrounding the origin, with a minimal number of contact points with the vector field. Moreover, the arguments are essentially topological, with no use of a desingularization theory, as it is the case in [D]. 2000 Mathematics Subject Classification : 34C05, 34A26.
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Submitted on : Wednesday, January 16, 2019 - 2:14:32 PM
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Robert Roussarie. A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES A tribute to Ivar Bendixson. 2019. ⟨hal-01983440⟩

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