A topological study of planar vector field singularities - Archive ouverte HAL
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2020

A topological study of planar vector field singularities

Résumé

In this paper one extends results of Bendixson [I] and Dumortier [2] about the germs of vector fields at the origin of IR2, which is assumed to be an singularity isolated from other singularities and periodic orbits as well. As a new tool, one uses minimal centred curves, which are curves surrounding the origin, with a minimal number of contact points with the vector field. A similar notion was introduced by Le Roux in [1]. It is noticeable that the arguments are essentially topological, with no use of a desingularization theory, as in [2] for instance.

Dates et versions

hal-03026336 , version 1 (26-11-2020)

Identifiants

Citer

Robert Roussarie. A topological study of planar vector field singularities. Discrete and Continuous Dynamical Systems - Series A, 2020, 40 (9), pp.5217-5245. ⟨10.3934/dcds.2020226⟩. ⟨hal-03026336⟩
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