Théorèmes d’approximation pour les sections différentiables

Resume Le principail résultat de ce travail est un Théorème d’approximation des sections différentiables d’un fibré linéaireF sur un espace analytique réel cohérentX. (I) On définit le concept de sections différentiables d’un tel fibré puis le faisceau des germes de sections différentiablesC ^∞ (F) qui s’identifie àF ^∞=F⊗ _Ox C _X ^∞ :F=dual du fibré linéaireF,C _X ^∞ =faisceau des germes de fonctions différentiables surX. (II)X est supposé en plus paracompact et localement compact. On construit surF ^∞(X) une ?topologie de Whitney? pour laquelleF(X) est dense dansF ^∞(X). La démonstration utilise les complexifiés et et les voisinages de Stein deX dans .

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Sunto Il risultato principale di questo lavoro è un teorema di approssimazione delle sezioni differenziabili di un fibrato lineareF su uno spazio analitico reale coerenteX. (I) Si definisce il concetto di sezione differenziabile di un tale fibrato poi il fascio dei germi delle sezioni differenziabiliC ^∞ (F) che si identifica aF ^∞=F⊗ _Ox C _X ^∞ :F=duale del fibrato lineareF,C _X ^∞ dei germi delle funzioni differenziabili suX. (II)X è supposto inoltre paracompatto e localmente compatto. Si costruisce suF ^∞ (X) una ?topologia di Whitney? per la qualeF(X è denso inF ^∞(X). La dimostrazione utilizza i complessificati e e gli intomi di Stein diX in .

     

Théorémes d'existence en optimisation non convexe

Some existence results in non convex optimization. In this article we give a method to solve, under suitable hy-pothesis , the class of problems of calculus of variations: where V i s a Sobolev space and ? a differential operator . We suppose no hypothesis of convexity on g .     

Théorèmes sur les groupes de substitutions

Sans résumé     

Théorèmes d'existence pour un modèle membranaire « proprement invariantde plaque non linéairement élastique

We establish the “local” existence of an injective solution to the nonlinear, “properly invariant”, membrane plate model, stated in [1] and [2], successively for the clamped plate submitted to forces parallel to its plane and for the plate submitted to a boundary condition of place of “extended” state.     

Théorèmes de Riemann–Roch pour les champs de Deligne–Mumford

We develop a cohomology theory for Deligne–Mumford stacks, adapted to Hirzebruch–Riemann–Roch formulas. For this, we define the cohomology with coefficients in the representations and a Chern character, and we prove a Grothendieck–Riemann–Roch formula for the associated Riemann–Roch transformation.     

Un critère de Darboux d'existence d'intégrale première pour les 1-formes différentielles analytiques

Resumé On considère une 1-forme analytique définie sur un ouvert borné de ⁿ et qui s'étend au voisinage de l'adhérence de cet ouvert. On montre que si elle possède une infinité de feuilles contenues dans des hypersurfaces algébriques différentes et de degrés bornés alors elle admet une intégrale première méromorphe. Si de plus l'origine est dans l'adhérence de chacune de ces feuilles alors la 1-forme admet une intégrale première méromorphe de graphe algébrique. Des exemples illustrent l'optimalité de ces résultats.

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Consider a germ of analytic differential one form and suppose there exists infinitely separatrix in algebraic surfaces of bounded degree. The conclusion is that there exists an algebraic first integral. We give a list of examples wich explain the necessity of the hypotheses.

Financements: CNRS et réseau européen TMR Sing. Eq. Diff. et Feuilletages     

Théorème de Poincaré–Alexander pour les domaines modèles

The Poincaré–Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of ${\mathbb{C}}^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains.     

Théorèmes de dualité pour les corps de fonctions sur des corps locaux supérieurs

Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. We define Tate-Shafarevich groups of a commutative group scheme via cohomology classes locally trivial at each completion of K coming from a closed point of X. We establish duality theorems between Tate-Shafarevich groups for finite groups schemes and for tori.     

Temps d'instabilité pour les perturbations de systèmes intégrables analytiques

For a positive integer n and $R>0$, we set $B_R^n=\{x\in {\mathbb{R}}^n|6x{6}_{\infty }<R\}$. Given $n?4$ and $R>1$ we construct a sequence of analytic perturbations $(H_j)$ of the completely integrable Hamiltonian $?(r)=\frac{1}{2}(r_1^2+?+r_{n?1}^2)+r_n$ on ${\mathbb{T}}^n\times B_R^n$, with unstable orbits for which we can estimate the time of drift in the action space. These functions $H_j$ are analytic on a fixed complex neighborhood V of ${\mathbb{T}}^n\times B_R^n$, and if ${?}_j\text{:}=6H_j??6_{C^0(V)}$ the time of drift of these orbits is smaller than $\exp (c{(1/{?}_j)}^{1/2(n?3)})$ for a fixed constant $c>0$. Our unstable orbits pass close to a doubly resonant surface, so the result is almost optimal since the stability exponent for such orbits is $1/2(n?2)$. To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens

We give a weak version of the Kolmogorov-Arnold-Moser theorem In the framework of Mather's theory of Lagrangian systems. A particular case has already been established by Lions, Papanicolaou and Varadhan.     

Théorèmes de finitude en cohomologie galoisienne

Sans résumé A Georges de Rham,à l’occasion de son soixantième anniversaire     

Quelques théorèmes centraux limites pour les mosaïques poissoniennes du plan

We prove central limit theorems for certain geometrical characteristics of the convex polygons determined by a standard Poisson line process in the plane, such as: the angles at the vertices of the polygons, the empirical mean of the number of vertices and the empirical mean of the perimeter of the polygons.     

Algorithmes parallèles asynchrones pour des systèmes singuliers

In this paper we give a convergence result concerning parallel bounded delayed asynchronous algorithms for linear fixed point problems with nonexpansive linear mappings with respect to a weighted maximum norm. This allows us to propose parallel algorithms which converge to the solution of consistent singular systems, including singular M-matrices (see for more details [3]). An important characteristic of our technical framework is that we are able to describe two-stage algorithms.     

Le théorème d'approximation pour les valuations deKrull

Sans résumé