Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.
In rings of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to , provided is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that...
Nous donnons une méthode pour calculer le nombre de cycles évanouissants d’une hypersurface complexe n’ayant pas nécessairement des singularités isolées.
In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.
Nous démontrons que la donnée de la forme de Seifert entière et de la fonction zêta de Denef-Loeser d’un germe de courbe plane à singularité isolée ne déterminent pas le type topologique de ce germe. De plus, la fonction zêta de Denef-Loeser d’un tel germe ne détermine pas la forme de Seifert entière associée.
In this paper we construct non-trivial examples of blow-analytic isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in , can be deformed via a rational blow- analytic isomorphism of , to a smooth analytic arc.