Astérisque - Parutions - 323 (2009) 41-59 < Parutions < 2009 < 323

Differential Equations and Singularities. 60 years of J. M. Aroca
Felipe Cano, Frank Loray, Juan José Moralez-Ruiz, Paulo Sad, Mark Spivakovsky, éditeurs
Astérisque 323 (2009), xxvii+487 pages
Acheter l'ouvrage
Présentation, Sommaire

On the limit of families of algebraic subvarieties with unbounded volume
César Camacho, Luiz Henrique de Figueiredo
Astérisque 323 (2009), 41-59

Résumé :
Sur la limite des familles de subvarietés algébriques sans volume borné
On prouve que la limite d'une suite d'ensembles semi-algébriques génériques donnés par un nombre fini de formules existe toujours et est un ensemble semi-algébrique, ensemble qui peut être donné explicitement comme une expression booléenne impliquant les primitives des formes additives de formules.

Mots-clefs : Ensembles semi-algébriques, équations différentielles ordinaires

Abstract:
We prove that the limit of a sequence of generic semi-algebraic sets given by a finite number of formulas always exists and is a semi-algebraic set that can be explicitly given as a Boolean expression involving the primitives of the additive forms of the formulas.

Keywords: Semi-algebraic sets, ordinary differential equations

Class. math. : 14P10; 14P15

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