Sur la vitesse d'explosion des points fixes paraboliques dans la famille quadratique

We define the asymptotic size of a parabolic fixed point, and link it to the speed of explosion into a cycle in some cases. For the fixed points of the quadratic family, we give a relation to the inner conformal radius of Siegel disks. Applications will be given in a further note. To cite this article: A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1107–1112.     

Nouvelle preuve d'un théorème de Yoccoz

If θ is an irrational real number such that ∑(lnq_n+1)/q_n=+∞ where p_n/q_n are the convergents of θ, then the quadratic polynomial $\text{P}{}_{\mathrm{\theta }}\text{(z)=}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>2\pi \theta </mtext>}}\text{z+z}{}^2$ is not linearizable at 0. This theorem has been proved in 1988 by J.C. Yoccoz, who first constructs a nonlinearizable germ by inverting a renormalisation procedure, and then proves universality of the quadratic family for that question. We give an alternative proof, based on the study of the explosion of parabolic cycles. To cite this article: A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

La conjecture de Karoubi pour la K-théorie lisse

Smooth K-functors are constructed on the category of locally convex real (resp. complex) algebras. The Karoubi's conjecture for the smooth K-theory on the isomorphism of algebraic and smooth K-functors is confirmed on the category of real (resp. complex) quasi-stable Fréchet algebras. To cite this article: H. Inassaridzé, T. Kandélaki, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Irréductibilité de la première équation de Painlevé

A definition of reducibility for algebraic codimension two foliations given by closed 2-forms is proposed. Reducible foliations are characterised on theirs Galois groupoids. We apply this to the foliation given by the first Painlevé equation. Its Galois groupoid is computed and this proves its irreducibility. To cite this article: G. Casale, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Fonctions rationnelles aux différences à valeurs entières dans les vecteurs de Witt

We transpose Kochen's results on integral valued rational functions over the p-adic numbers to difference rational functions over the Witt vectors with their Frobenius. To cite this article: L. Bélair, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Relation de Rankine Hugoniot faible pour les lois de conservation avec contraintes primitives convexes

We describe a Weak Rankine Hugoniot relation for constrained discontinuous solutions of conservation laws. The constraint is convex in the primitive variable. Various examples show the potential interest of this approach. To cite this article: B. Després, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Opérateurs de Fuchs non linéaires

In this Note, we study nonlinear partial differential equations of Fuchs type in spaces of functions sufficiently differentiable with respect to the Fuchsian variable and in Gevrey spaces with respect the other variables. The results are a generalization of those of Baouendi–Goulaouic obtained in the analytic case. To cite this article: P. Pongérard, C. Wagschal, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Moyennes empiriques pour les mosaïques de Voronoi du disque de Poincaré

Let Φ be a stationary ergodic point process with finite intensity of the Poincaré disk. After defining the typical cell associated to the Voronoi tessellation of Φ, we study the convergence of empirical means of this tessellation. Contrary to the Euclidean case, several natural choices of means exist, leading to different behavior. The case where Φ is a Poisson process is more specifically characterized. To cite this article: F. Lips, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Sur les automorphismes du groupe de Cremona

We describe the group of automorphisms of the Cremona group. To cite this article: J. Déserti, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Modules de cycles et motifs mixtes

For a perfect field k, we give a relation between the category of homotopy invariant sheaves with transfers defined by Voevodsky and the category of cycle modules defined by Rost. More precisely, the category of cycle modules over k is equivalent to the category obtained from the homotopy invariant sheaves with transfers by formally inverting the sheaf represented by $\text{G}{}_{\mathrm{m}}$ with its canonical structure of a presheaf with transfers. This gives a canonical monoidal structure on the category of cycle modules over k, and shows that it is Abelian. To cite this article: F. Déglise, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Diffraction et mesure de Palm des processus ponctuels

Using the notion of Palm measure, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes: stochastic subsets of $\text{Z}{}^{\mathrm{d}}$, sets obtained by the “cut-and-project” method. To cite this article: J.-B. Gouéré, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Une axiomatisation de la substitution

We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

La condensation de la matrice masse,ou mass-lumping,pour les éléments finis mixtes de Raviart–Thomas–Nédélec d'ordre 1

. We present practical means to obtain a positive diagonal matrix for the first order Raviart–Thomas–Nédélec finite elements. Applying it to the second order Maxwell equations allows us to use explicit time schemes to solve the resulting differential system. To cite this article: P. Lacoste, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Sur un modèle markovien rudimentaire de diffusion atomique

We introduce and study an interacting particle system. The evolution is Markovian. The elementary step of the dynamics is the following: one point is randomly chosen in the ambient space, the nearest particle moves to that point. We investigate in particular equilibrium properties of the system. To cite this article: J.-B. Gouéré, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Cellules de Kazhdan–Lusztig et correspondance de Robinson–Schensted

Kazhdan and Lusztig have introduced (left, right and two-sided) cells in an arbitrary Coxeter group. For the symmetric group, they showed that these cells are given by the Robinson–Schensted correspondence. Here, we describe a Robinson–Schensted correspondence for the complex reflection groups G(e,1,n). In a recent joint work with C. Bonnafé, we have shown that, in the case e=2 (where G(2,1,n) is the Coxeter group of type B_n), this correspondence determines the Kazhdan–Lusztig cells with respect to certain unequal parameters. To cite this article: L. Iancu, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Cohomologie des groupes localement compacts et produits tensoriels continus de représentations

The following is an expository paper, containing few and sometimes incomplete proofs, on continuous tensor products of Hilbert spaces and of group representations, and on the irreducibility of the latter; the principal results in the last direction are due to Verchik, Gelfand, and Graiev. The theory of continuous tensor products of Hilbert spaces, based on a fundamental theorem of Araki and Woods, is closely related to that of conditionally positive definite functions; it relies on the technique of symmetric Hilbert spaces, which also can be used to give a new proof of the classical Lévy-Khinchin formula (see A. Guichardet, (1973). J. Multiv.3 249–261.). Another basic tool for what follows is the 1-cohomology of unitary representations of locally compact groups; here, the main results are due to P. Delorme; let us mention, for instance, his results for the case of a group G containing a compact subgroup K such that $\text{L}{}^1\text{(Kβ}\text{G}\text{K}\text{)}$ is commutative, using a Lévy-Khinchin's type formula for K-invariant functions due to Gangolli, Faraut, and Harzallah. We add that the results exposed in that paper should have interesting connections with the central limit theorems à la Parthasarathy-Schmidt (see K. Parthasarathy, (1974). J. Multiv. Anal.4 123–149).     

Fluctuation des processus de Lévy et dispersion ( « scattering »)

We show a strong connexion between the problem of fluctuations of Lévy processes and scattering theory. To cite this article: S. Fourati, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Solutions sous-analytiques globales de certaines équations d'Hamilton–Jacobi

In the 1980 Crandall and Lions introduced the concept of viscosity solution in order to get existence and/or unicity results for Hamilton–Jacobi equations. In this Note we focus on the Dirichlet problem for Hamilton–Jacobi equations stemming from calculus of variations, and assert that if the data are analytic then the viscosity solution is moreover subanalytic. We extend this result to generalized eikonal equations, stemming from sub-Riemannian geometry problems. To cite this article: E. Trélat, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Construction inconditionnelle de groupes de Galois motiviquesAn unconditional construction of motivic Galois groups

We attach to any “classical” Weil cohomology theory over a field a motivic Galois group, defined up to an inner automorphism. We also study the specialisation of numerical motives and the behaviour of motivic Galois group by specialisation. To cite this article: Y. André, B. Kahn, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 989–994.     

Équations aux différences dans les vecteurs de Witt

We prove an approximation property for Frobenius difference equations in the Witt vectors, analog to a theorem of Greenberg [Publ. Math. IHES 31 (1966) 59–64]. To cite this article: L. Bélair, C. R. Acad. Sci. Paris, Ser. I 340 (2005).