Publications

2009

• On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials
  
  • Eliasson Hakan
  • Kuksin Sergei
  Communications in Mathematical Physics, Springer Verlag, 2009, 286 (1), pp.125-135. We prove that a linear d-dimensional Schrödinger equation with an x-periodic and t-quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of x-periodic functions. This transformation is a quasiperiodic function of t. (10.1007/s00220-008-0683-2)
  DOI : 10.1007/s00220-008-0683-2
• Geodesics in the space of measure-preserving maps and plans
  
  • Ambrosio Luigi
  • Figalli Alessio
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2009, 194 (2), pp.421-462. We study Brenier's variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the properties of the relaxed distance, we show a close link between the Lagrangian and the Eulerian model, and we derive necessary and sufficient optimality conditions for minimizers. These conditions take into account a modified Lagrangian induced by the pressure field. Moreover, adapting some ideas of Shnirelman, we show that, even for non-deterministic final conditions, generalized flows can be approximated in energy by flows associated to measure-preserving maps. (10.1007/s00205-008-0189-2)
  DOI : 10.1007/s00205-008-0189-2
• Laure Saint-Raymond reçoit un prix de la Société Mathématiques Européenne
  
  • Gallagher Isabelle
  • Golse François
  Gazette des Mathématiciens, Société Mathématique de France, 2009, 120, pp.82-84.
• Vibrations chaotiques et grosses balafres
  
  • Anantharaman Nalini
  • Nonnenmacher Stéphane
  Gazette des Mathématiciens, Société Mathématique de France, 2009, 119, pp.16-32.
• Corps de nombres peu ramifies et formes automorphes autoduales
  
  • Chenevier Gaëtan
  • Clozel Laurent
  Journal of the American Mathematical Society, American Mathematical Society, 2009, 22 (2), pp.467-519. Let S be a finite set of primes, p in S, and Q_S a maximal algebraic extension of Q unramified outside S and infinity. Assume that |S|>=2. We show that the natural maps Gal(Q_p^bar/Q_p) --> Gal(Q_S/Q) are injective. Much of the paper is devoted to the problem of constructing selfdual automorphic cuspidal representations of GL(2n,A_Q) with prescribed properties at all places, that we study via the twisted trace formula of J. Arthur. The techniques we develop shed also some lights on the orthogonal/symplectic alternative for selfdual representations of GL(2n).