Équation homologique et cycles asymptotiques d'une singularité nœud-col

Let a germ of holomorphic vector field Z be given and assume that is an isolated degenerate-resonnant singular point for Z (one and only one non-zero eigenvalue). Such a vector field acts as a derivative over the space of holomorphic germs at the origin of the complex plane. We obtain the solutions of the homological equation Z·F=G by integrating G along some asymptotic paths tangent to the complex trajectories of Z and ending at the singularity; this locate the obstructions to solve such an equation in the period of G along asymptotic cycles. The Borel transform is thus extended to the foliated setting and this geometrical approach helps us in the study of the conjugacy problem. For instance we find without expense of computation the obstructions obtained previously by P.M. Elizarov for the Poincaré-Dulac models. This approach of the caracteristics method in the singular setting will lead us, in a further print, to describe the analytical classification of germs of degenerate-resonnant vector fields.     

Equivalence d'une couronne de barres de combustible et d'une surface active

Sans résuméSubside N^o 4353 du Fonds national suisse de la recherche scientifique.     

Remarques sur le spectre des longueurs d'une surface et comptages

Resumé Nons nous intéressons au spectre des longueurs associé à une variété de courbure négative. Nous démontrons que le spectre des longueurs d'une surface n'est pas inclus dans un sous-groupe discret de . Nous comparons également le spectre des longueurs de différentes structures Riemanniennes sur une même variété.

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This paper deals with the length spectrum associated to a negatively curved manifold. In particular we prove that the length spectrum of a surface is not included in a discret subgroup of . We also compare the length spectrum for different Riemannian structures.

     

Endomorphisme de bascule et courbure areolaire d'une sous-variete d'une variete riemannienne

Sans résumé     

Sur les variations faibles et fortes d'une fonctionnelle

Sans résumé Il Comitato Organizzatore ?.     

Platitude d'une adherence schematique et lemme de Hironaka generalise

The main aim of this article is to prove the following:Theorem (Generalized Hironaka's lemma). Let X→Y be a morphism of schemes, locally of finite presentation, x a point of X and y=f(x). Assume that the following conditions are satisfied:

1. O _Y,y is reduced.
2. f is universally open at the generic points of the components of X_y which contain x.
3. For every maximal generisation y′ of y in Y and every maximal generisation x′ of x in X which belongs to X_y, we have dim_x, (X_y')=dim_x(X_y)=d.
4. X_y is reduced at the generic points of the components of X_y which contain x and (X_y)_red is geometrically normal over K(y) in x.

Then there exist an open neighbourhood U of x in X and a subscheme U₀ of U which have the same underlying space as U such that f₀:U₀\arY is normal (i.e. f₀ is a flat morphism whose geometric fibers are normal).     

Support d’asymptotiques et croissance des fonctions propres sur un espace symétrique semi-simple

We associate several distribution boundary values to an eigenfunction with moderate growth on a riemannian symmetric space G/K; the associated character of the algebra D(G/K) of invariant differential operators is allowed to be non-regular. We prove results on the support of these boundary values. These allow us to recover the theorems of Matsuki-Oshima and Oshima on the equivalence between growth of an eigenfunction and limitations on the supports of its boundary values. Our approach is based on an asymptotic analysis that makes no use of hyperfunction theory.     

Sur le groupe des homographies et des antihomographies d'une variable complexe

Sans résumé     

Propriétés différentielles d'une fonction et approximation

Sans résumé