Résurgence des systèmes différentiels linéaires et calcul des matrices de Stokes

Abstract : The aim of this thesis is the construction of a method of effective calculation of Stokes multipliers with error estimation. This method applies itself to all systems with single level and the first level of systems with multiple levels. In a theoretical part, we begin by stating the resurgence of formal solutions following Ecalle's method by regular perturbation and majorant series. We deduce from it a precise description of singularities in the Borel plane determining the resurgence coefficients. We make then explicit formulae between these resurgence coefficients and the Stokes multipliers. In the numerical part, we suppose that the entries of the systems are rational and we choose to work in the Borel plane where we calculate the resurgence coefficients by successive analytic continuations. In particular, we build algorithms in order to estimate the error. We give too several numerical examples.
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  • HAL Id : tel-00351882, version 1

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Pascal Rémy. Résurgence des systèmes différentiels linéaires et calcul des matrices de Stokes. Mathématiques [math]. Université d'Angers, 2007. Français. ⟨tel-00351882⟩

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