ECALLE, Jean - Analyse Harmonique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
| Nous introduisons un appareil analytique (fonctions spéciales, monomes de résurgence, etc) permettant de mener à bien la synthèse canonique des "Objets Analytiques Locaux" (difféos, champs de vecteurs, EDOs etc), autrement dit, de construire, au sein de chaque classe de conjugaison, un reprèsentant clairement privilégie et aux propriétès ("antipodalite" etc) assez inattendues. |
Abstract :
| Until very recently, received wisdom seemed to discount the feasibility of a truly canonical and completely explicit synthesis for Local Analytic Objects, that is to say the possibility of constructing privileged representatives in each analytic conjugacy class of such objects. But in the mid 90s it emerged that there does exist a canonical synthesis after all. We call it paralogarithmic, because its building blocks are a new class of transcendental functions, the so-called paralogarithms, quite distinct from the classical but (in this context) unsuitable hyperlogarithms. We also call it spherical, because the most salient feature of the objects thus produced is a tendency to extend to the whole Riemann sphere and to go in pairs : a direct object, and its antipodal reflection. Both objects --- direct and antipodal --- always exist; are indisputably canonical upto the choice of one unremovable parameter (the "twist" c); and connect under analytic continuation "whenever the invariants permit". |
Article :
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Contact : Jean.Ecalle@math.u-psud.fr