Titre : | Concerning the Hilbert 16th problem | Type de document : | texte imprimé | Auteurs : | Yu ILYASHENKO, Editeur scientifique ; S. YAKOVENKO, Editeur scientifique | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | Année de publication : | Cop. 1995 | Collection : | American Mathematical Society Translations. Series 2, ISSN 0065-9290 num. 165 | Importance : | VII-219 p. | ISBN/ISSN/EAN : | 978-0-8218-0362-2 | Langues : | Anglais (eng) Langues originales : Russe (rus) | Catégories : | 34C05 34C20
| Mots-clés : | 16e problème de Hilbert | Résumé : | Six papers consider qualitative properties of vector fields on the plane, particularly bifurcations of limit cycles of planar vector fields and the desingularization of singular points for individual vector fields and for analytic families of such fields. An introduction to Hilbert's sixteenth problem is followed by discussions of the finite cyclicity of elementary polycycles in generic families, desingularization in families of analytic differential equations, the order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity, few-parameter generic families of vector fields on the two-dimensional sphere, and geometric proof of the Bautin theorem. | Note de contenu : | références |
Concerning the Hilbert 16th problem [texte imprimé] / Yu ILYASHENKO, Editeur scientifique ; S. YAKOVENKO, Editeur scientifique . - American Mathematical Society, Cop. 1995 . - VII-219 p.. - ( American Mathematical Society Translations. Series 2, ISSN 0065-9290; 165) . ISBN : 978-0-8218-0362-2 Langues : Anglais ( eng) Langues originales : Russe ( rus) Catégories : | 34C05 34C20
| Mots-clés : | 16e problème de Hilbert | Résumé : | Six papers consider qualitative properties of vector fields on the plane, particularly bifurcations of limit cycles of planar vector fields and the desingularization of singular points for individual vector fields and for analytic families of such fields. An introduction to Hilbert's sixteenth problem is followed by discussions of the finite cyclicity of elementary polycycles in generic families, desingularization in families of analytic differential equations, the order of the topologically sufficient jet of a smooth vector field on the real plane at a singular point of finite multiplicity, few-parameter generic families of vector fields on the two-dimensional sphere, and geometric proof of the Bautin theorem. | Note de contenu : | références |
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