A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES
| Affiliation auteurs | Affiliation ok |
| Titre | A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES |
| Type de publication | Journal Article |
| Year of Publication | 2020 |
| Auteurs | Roussarie R |
| Journal | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS |
| Volume | 40 |
| Pagination | 5217-5245 |
| Date Published | SEP |
| Type of Article | Article |
| ISSN | 1078-0947 |
| Mots-clés | contact index, minimal centred curve, Phase portrait, Planar vector field singularities, sectoral decomposition |
| 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. |
| DOI | 10.3934/dcds.2020226 |