Caractérisation des feuilletages holomorphes singuliers, contenus dans des feuilletages Levi flat, sur les surfaces complexes compactes

Let be a holomorphic foliation with reduced singularities on a complex surface M and a real analytic codimension one foliation on M whose leaves contain the ones of . We show that a Levi flat group of diffeomorphisms of is resoluble and holomorphically conjugate to his normal form. We deduce, in one hand, that each singularity of  is conjugate to his normal form. In the other hand at each singularity m of , where is not defined, up a conjugacy, by the one form ω=xdy+ydx, one of the local invariant curves of , with non obvious holonomy, is contained in the set of singularities of . Moreover if M is a compact Stein variety we show, under some generic conditions, that has a 1-Liouvillian first integrating factor.     

Le saut en zéro de la fonction de décalage spectral

We give a formula for the jump at zero of the spectral shift function associated with Schrödinger operator on manifolds with conical ends. We show that, according to its decay, a zero energy resonant state has a non-integer contribution.     

Équidistribution presque partout modulo 1 de suites oscillantes perturbées III : cas liouvillien multidimensionnel

We extend the results of uniform distribution modulo 1 given in [B. Rittaud, Équidistribution presque partout modulo 1 de suites oscillantes perturbées, Bull. Soc. Math. France 128 (2000) 451-471; B. Rittaud, Équidistribution presque partout modulo 1 de suites oscillantes perturbées, II: Cas Liouvillien unidimensionnel, Colloq. Math. 96 (1) (2003) 55-73], which deal with sequences of the form , where n(hn), and are polynomially increasing sequences, n(εn) a bounded sequence, essentially a C³-function Zd-periodic, Θ an element of Rd and t a real number. We remove the Diophantine hypothesis on Θ needed in [the first of above mentioned articles], and add a technical hypothesis on hn. We apply this result to the convergence of diagonal averages for d×d matrices.     

Sur le changement de base stable des intégrales orbitales pondérées

Let G^′ be a quasi-split connected reductive group over a p-adic field F. Let E be a cyclic extension of F. In the context of cyclic base change, we can attach to G^′ and E a twisted space G^* (in the sense of Labesse). Let G be an inner form of G^*. If G^′ is GL(n), SL(n) or more generally a group which we call L-stable, we define and prove the existence of a non-invariant transfer between the weighted orbital integrals of G and those of G^′. For GL(n), such a transfer has been conjectured by Labesse. The proof is based on previous results of harmonic analysis on Lie algebras and on a generalization of a result of Waldspurger concerning Arthur's (G,M)-families.     

Dérivées de Lie des spineurs

Résumé On étudie le problème de la transformation d'un champ de spineurs sur une variété spinorielle par un groupe à un paramètre de difféomorphismes de la variété, en généralisant aux champs de spineurs la notion de dérivation de Lie. On peut alors étudier l'invariance d'un système d'équations aux dérivées partielles sur les spineurs (équations de Dirac) avec des méthodes analogues à celles qui sont valables dans le cas des tenseurs (équations de Maxwell).

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Summary The notion of a Lie derivative is generalized to spinor fields on a Spin manifold and the problem of transforming a spinor field under a one-parameter group of diffeomorphisms of the manifold is studied. The invariance of a differential system acting on spinors (Dirac's equations) is studied using methods similar to those used in the case of tensors (Maxwell's equations).

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Actuellement: Université des Sciences et Techniques de Lille.

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Entrata in Redazione il 19 aprile 1971.     

Comportement asymptotique des structures formées de plaques

After having introduced different decompositions of the displacements of a plate and of a structure made of plates, we give the asymptotic behavior of this structure. To cite this article: G. Griso, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Equations des variétés de Kummer

Sans résumé

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Mesure de concentration et de mobilité des porteurs des zones diffusées dans le Si

Sans résumé     

Hauteurs normalisées des sous-variétés de produits de modules de Drinfeld

After establishing some important results on the usual height of projective varieties in positive characteristic, we construct a normalized height for subvarieties of products of Drinfeld modules and investigate its properties. In case the Drinfeld modules are pairwise isogeneous, we obtain in particular that the normalized height vanishes exactly on torsion varieties, that is on translates of sub-T-modules by torsion points.     

Spectral Criteria of Abstract Sequences; Application to Difference Equations

We suppose that M is a closed subspace of l ^∞(J, X), the space of all bounded sequences {x(n)} _n?J ? X, where J ? {Z⁺,Z} and X is a complex Banach space. We define the M-spectrum σ_M (u) of a sequence u ? l ^∞(J,X). Certain conditions will be supposed on both M and σ_M (u) to insure the existence of u ? M. We prove that if u is ergodic, such that σ_M (u,) is at most countable and, for every λ ? σ_M (u), the sequence e^?iλnu(n) is ergodic, then u ? M. We apply this result to the operator difference equationu(n + 1) = Au(n) + ψ(n), n ? J,and to the infinite order difference equation Σ ^r _k=1 a_k (u(n + k) ? u(n)) + Σ _{s ? Z}?(n ? s)u(s) = h(n), n?J, where ψ?l ^∞(Z,X) such that ψ| _J ? M, A is the generator of a C ₀-semigroup of linear bounded operators {T(t)} _t>0 on X, h ? M, ? ? l ¹(Z) and a_k ?C. Certain conditions will be imposed to guarantee the existence of solutions in the class M.     

Variétés de Kummer généralisées

Re?u le 22 mars 2001; forme finale: 18 juin 2001 / Published online: 1 February 2002     

Singularities of the Minkowski set and affine equidistants for a curve and a surface

Generic singularities of envelopes of families of chords and bifurcations of affine equidistants defined by a pair of a curve and a surface in R³ are classified. The chords join pairs of points of the curve and the surface such that the tangent line to the curve is parallel to the tangent plane to the surface. The classification contains singularities of stable Lagrange and Legendre projections, boundary singularities and some less known classes appearing at the points of the surface and the curve themselves.     

Bifurcation diagrams and caustics of simple quasi border singularities

Quasi boundary and quasi corner singularities of functions are discussed. They correspond to the classifications of Lagrangian projections with a boundary or a corner. The geometry of bifurcation diagrams and caustics of simple quasi boundary and quasi corner singularities in R³ and R⁴ are described.     

Classification des algèbres de Lie graduées simples de croissance ≦1

Sans résumé     

Simple tangential family germs and perestroikas of their envelopes

A tangential family is a 1-parameter system of regular curves emanating tangentially from another regular curve. We classify simple tangential family germs up to A-equivalence. We describe perestroikas of envelopes of simple tangential family germs of small codimension under small deformations of the germ among tangential families.     

Distorsion des distances dans les groupes de Lie nilpotents

Let G be a connected nilpotent Lie group and H a connected subgroup of G. We give an explicit formula for the distance to the origin with the exponential coordinates of the second kind of g∈G. Using this fact, we prove that the distance to the origin of any element in H is bounded by a polynomial function of the distance to the origin in the group G. The degree of the polynomial is the nilpotency rank of the group G.     

Majorations de Chernoff pour des chaînes de Markov contrÔlées

Résumé Let but de cet article est d'établir des majorations de Chernoff pour des chaÎnes de Markov contrÔlées, semblables à celles de Donsker et Varadhan [1] pour les chaÎnes non contrÔlées. On applique les résultats obtenus à un problème de gain optimal en moyenne sous contraintes.Dans un article ultérieur, on exposera une application à des problèmes de tests séquentiels.