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

Robert Roussarie (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Sectoral decomposition; minimal curve; contact index

Domaines: Systèmes dynamiques [math.DS]

Robert Roussarie. A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES A tribute to Ivar Bendixson. 2019. ⟨hal-01983440⟩