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H 1 Nonlinear analysis with resurgent functions

Auteurs : Sauzin, David (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Ecalle’s resurgent functions appear naturally as Borel transforms of divergent series like Stirling series, formal solutions of differential equations like Euler series, or formal series associated with many other problems in Analysis and dynamical systems. Resurgence means a certain property of analytic continuation in the Borel plane, whose stability under con- volution (the Borel counterpart of multiplication of formal series) is not obvious. Following the analytic continuation of the convolution of several resurgent functions is indeed a delicate question, but this must be done in an explicit quan- titative way so as to make possible nonlinear resurgent calculus (e.g. to check that resurgent functions are stable under composition or under substitution into a convergent series). This can be done by representing the analytic continuation of the convolution product as the integral of a holomorphic n-form on a singular n-simplex obtained as a suitable explicit deformation of the standard n-simplex. The theory of currents is convenient to deal with such integrals of holomorphic forms, because it allows to content oneself with little regularity: the deformations we use are only Lipschitz continuous, because they are built from the flow of non-autonomous Lipschitz vector fields.

    Codes MSC :
    30D05 - Functional equations in the complex domain, iteration and composition of analytic functions
    37FXX - complex dynamical systems

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 25/06/15
      Date de captation : 12/06/15
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 00:55:29
      Domaine : Dynamical Systems & ODE ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-06-12_Sauzin.mp4

    Informations sur la rencontre

    Nom de la rencontre : Real analytic geometry and trajectories of vector fields / Géométrie analytique réelle et trajectoires de champs de vecteurs
    Organisateurs de la rencontre : Kurdyka, Krzysztof ; Parusinski, Adam ; Rolin, Jean-Philippe ; Sanz, Fernando
    Dates : 08/06/15 - 12/06/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1220.html

    Citation Data

    DOI : 10.24350/CIRM.V.18772403
    Cite this video as: Sauzin, David (2015). Nonlinear analysis with resurgent functions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18772403
    URI : http://dx.doi.org/10.24350/CIRM.V.18772403


    Bibliographie

    1. Sauzin, D. (2012). Nonlinear analysis with resurgent functions. - https://hal.archives-ouvertes.fr/hal-00766749

    2. Sauzin, D. (2013). Introduction to 1-summability and resurgence. - https://hal.archives-ouvertes.fr/hal-00766749

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