Publications

2008

• Une nouvelle analyse des mesures maximisant l'entropie des difféomorphismes d'Anosov de surfaces
  
  • Buzzi Jerome
  , 2008. This note illustrates the strategy of our paper on piecewise affine surface homeomorphisms by giving a new proof of the finite multiplicity of the maximum entropy measure of Anosov diffeomorphisms (here on surfaces). This approach avoids the explicit construction of Markov partitions and will be applied elsewhere to some non-uniformly hyperbolic diffeomorphisms.
• Modular classes of Lie algebroid morphisms
  
  • Kosmann-Schwarzbach Yvette
  • Laurent-Gengoux Camille
  • Weinstein Alan
  Transformation Groups, Springer Verlag, 2008, 13 (3-4), pp.727-755. We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms associated to Lie algebroid extensions. We also define generalized morphisms, including Morita equivalences, that act on the 1-cohomology, and observe that the relative modular class is a coboundary on the category of Lie algebroids and generalized morphisms with values in the 1-cohomology. (10.1007/s00031-008-9032-y)
  DOI : 10.1007/s00031-008-9032-y
• Pseudodifferential operators and weighted normed symbol spaces.
  
  • Sjostrand Johannes
  Serdica Mathematical Journal, Bulgarian Academy of Sciences, Institute of Mathematics, 2008, pp.1-38.
• On some completions of the space of Hamiltonian maps
  
  • Humilière Vincent
  Bulletin de la société mathématique de France, Société Mathématique de France, 2008, 136 (3), pp.373-404. We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances. This allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous Hamiltonians. We also prove that some dynamical properties of Hamiltonian systems are preserved in the completions.
• An elementary proof of Blundon's inequality
  
  • Dospinescu Gabriel
  • Lascu Mircea
  • Pohoata Cosmin
  • Tetiva Marian
  Journal of Inequalities in Pure and Applied Mathematics, School of Communications and Informatics, 2008, 9 (4), pp.Article 100. In this note, we give an elementary proof of Blundon's Inequality. We make use of a simple auxiliary result, provable by only using the Arithmetic Mean - Geometric Mean Inequality.
• The six operations for sheaves on Artin stacks II: Adic Coefficients
  
  • Laszlo Yves
  • Olsson Martin
  Publications Mathématiques de L'IHÉS, IHÉS, 2008, 107, pp.169-210. In this paper we develop a theory of Grothendieck's six operations for adic constructible sheaves on Artin stacks continuing the study of the finite coefficients case in math.AG/0512097.
• Les équations d'Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l'équation de Gross-Pitaevskii
  
  • Danchin Raphaël
  • Bethuel Fabrice
  • Gravejat Philippe
  • Saut Jean-Claude
  • Smets Didier
  , 2010, Séminaire: Équations aux Dérivées Partielles. 2008-2009 (1), pp.12 pages. Dans cet exposé, on expose plusieurs résultats récents concernant la dynamique onde longue pour l'équation de Gross-Pitaevskii
• Scaling-sharp dispersive estimates for the Korteweg-de Vries group
  
  • Côte Raphaël
  • Vega Luis
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2008, 346, pp.845-848. We prove weighted estimates on the linear KdV group, which are scaling sharp. This kind of estimates are in the spirit of that used to prove small data scattering for the generalized KdV equations. (10.1016/j.crma.2008.05.003)
  DOI : 10.1016/j.crma.2008.05.003
• Familles de représentations de de Rham et monodromie p-adique
  
  • Berger Laurent
  • Colmez Pierre
  Asterisque, Société Mathématique de France, 2008, 319, pp.303-337. On donne une formalisation de la méthode de Sen pour les représentations $p$-adiques. Comme application de ces techniques, on montre que (1) toute représentation $p$-adique est surconvergente (2) si on se donne un espace $\calX = \mathrm{Spm}(S)$ qui paramétrise des représentations $p$-adiques $V_x$, alors l'ensemble des $x$ tels que $V_x$ est de de Rham (ou semi-stable, ou cristalline) á poids de Hodge-Tate dans un intervalle $[a,b]$ fixé est un sous-espace $S$-analytique de $\calX$ et (3) les modules de Fontaine $\mathrm{D}_*(V)$ associés varient analytiquement.
• A direct approach to Bergman kernel asymptotics for positive line bundles.
  
  • Sjostrand Johannes
  Arkiv för Matematik, 2008, pp.197-217.
• Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators.
  
  • Sjostrand Johannes
  Mathematische Annalen, Springer Verlag, 2008, pp.177-243.
• An explicit stationary phase formula for the local formal Fourier-Laplace transform
  
  • Sabbah Claude
  , 2008, pp.309-330. We give an explicit formula (i.e., a formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. This is a complex analogue of the formulas in the preprint math/0702436v1.
• Fourier-Laplace transform of a variation of polarized complex Hodge structure
  
  • Sabbah Claude
  Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2008, pp.123-158. We show that the Fourier-Laplace transform of a regular holonomic module over the Weyl algebra of one variable, which generically underlies a variation of polarized Hodge structure, underlies itself an integrable variation of polarized twistor structure.
• Kostant partitions functions and flow polytopes.
  
  • Vergne Michèle
  Transformation Groups, Springer Verlag, 2008, pp.447-469.
• Asymmetric equilibria in dynamic two-sided matching markets with independent preferences.
  
  • Sjostrand Johannes
  International Journal of Game Theory, Springer Verlag, 2008, pp.421-440.
• A Proof of Gromov's Algebraic Lemma
  
  • Burguet David
  Israel Journal of Mathematics, Springer, 2008, 168 (1), pp.291-316. Following the analysis of differentiable mappings of Y. Yomdin, M. Gromov has stated a very elegant "Algebraic Lemma" which says that the "differentiable size" of an algebraic subset may be bounded in terms only of its dimension, degree and diameter. We give a complete and elementary proof of Gromov's result using the ideas presented in his Bourbaki talk as well as other necessary ingredients. (10.1007/s11856-008-1069-z)
  DOI : 10.1007/s11856-008-1069-z
• The six operations for sheaves on Artin stacks I: Finite Coefficients
  
  • Laszlo Yves
  • Olsson Martin
  Publications mathematiques de l' IHES, IHES, 2008, 107, pp.109-168. In this paper we develop a theory of Grothendieck's six operations of lisse-étale constructible sheaves on Artin stacks of finite type over $S$, or more generally for a slightly more general class of stacks, called \emph{nice} stacks, which are not necessarily quasi--compact.
• Entropy methods for the Boltzman Equation
  
  • Olla Stefano
  • Golse François
  • Villani Cédric
  • Rezakhanlou Fraydoun
  , 2008, pp.107. (10.1007/978-3-540-73705-6)
  DOI : 10.1007/978-3-540-73705-6
• Khasminskii--Whitham averaging for randomly perturbed KdV equation
  
  • Piatnitski Andrey L.
  • Kuksin Sergei
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2008, 89 (4), pp.400-428. We consider the damped-driven KdV equation $$ \dot u-\nu{u_{xx}}+u_{xxx}-6uu_x=\sqrt\nu \eta(t,x), x\in S^1, \int u dx\equiv \int\eta dx\equiv0, $$ where $0<\nu\le1$ and the random process $\eta$ is smooth in $x$ and white in $t$. For any periodic function $u(x)$ let $ I=(I_1,I_2,...) $ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. We prove that if $u(t,x)$ is a solution of the equation above, then for $0\le t\lesssim\nu^{-1}$ and $\nu\to0$ the vector $ I(t)=(I_1(u(t,\cdot)),I_2(u(t,\cdot)),...) $ satisfies the (Whitham) averaged equation. (10.1016/j.matpur.2007.12.003)
  DOI : 10.1016/j.matpur.2007.12.003
• Random Kick-Forced 3D Navier-Stokes Equations in a Thin Domain
  
  • Chueshov Igor
  • Kuksin Sergei
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2008, 188 (1), pp.117-153. We consider the Navier-Stokes equations in the thin 3D domain T2×(0,ϵ) , where T2 is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly, when ε ≪ 1, the equation has a unique stationary measure and, secondly, after averaging in the thin direction this measure converges (as ε → 0) to a unique stationary measure for the Navier-Stokes equation on T2 . Thus, the 2D Navier-Stokes equations on surfaces describe asymptotic in time, and limiting in ε, statistical properties of 3D solutions in thin 3D domains. (10.1007/s00205-007-0068-2)
  DOI : 10.1007/s00205-007-0068-2
• Stochastic 3D Navier-Stokes equations in a thin domain and its α -approximation
  
  • Chueshov Igor
  • Kuksin Sergei
  Physica D: Nonlinear Phenomena, Elsevier, 2008, 237 (10-12), pp.1352-1367. In the thin domain Oε=T2×(0,ε), where T2 is a two-dimensional torus, we consider the 3D Navier-Stokes equations, perturbed by a white in time random force, and the Leray αα-approximation for this system. We study ergodic properties of these models and their connection with the corresponding 2D models in the limit ε→0. In particular, under natural conditions concerning the noise we show that in some rigorous sense the 2D stationary measure μμ comprises asymptotical in time statistical properties of solutions for the 3D Navier-Stokes equations in Oε, when ε≪1. (10.1016/j.physd.2008.03.012)
  DOI : 10.1016/j.physd.2008.03.012
• Commuting Hamiltonians and multi-time Hamilton-Jacobi equations
  
  • Cardin Franco
  • Viterbo Claude
  Duke Mathematical Journal, Duke University Press, 2008, 144 (2), pp.235-284. We prove that if a sequence of pairs of smooth commuting Hamiltonians converge in the $C^0$ topology to a pair of smooth Hamiltonians, these commute. This allows us define the notion of commuting continuous Hamiltonians. As an application we extend some results of Barles and Tourin on multi-time Hamilton-Jacobi equations to a more general setting. (10.1215/00127094-2008-036)
  DOI : 10.1215/00127094-2008-036
• Spectral instability for non-selfadjoint operators
  
  • Sjostrand Johannes
  , 2008, pp.265-273.
• Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications.
  
  • Sjostrand Johannes
  International Mathematics Research Notices, Oxford University Press (OUP), 2008, pp.48 pp.
• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
  
  • Côte Raphaël
  • Kenig Carlos
  • Merle Frank
  Communications in Mathematical Physics, Springer Verlag, 2008, 284 (1), pp.203-225. We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the solution is constant in time, or the solution scatters in infinite time. (10.1007/s00220-008-0604-4)
  DOI : 10.1007/s00220-008-0604-4