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Réduction et intégration symbolique des systèmes d'équations différentielles non-linéaires

Abstract : This thesis deals with symbolic integration and reduction of systems of autonomous nonlinear ordinary differential equations. The systems are studied locally in the neighbourhood of a regular or a singular point. In order to integrate them the considered systems are reduced by transformations such as blowing-ups and power transformations and normal form constructions. These methods allow to locally integrate any 2-dimensional system and non-nilpotent 3-dimensional systems. For higher dimensional systems and nilpotent 3-dimensional systems some further algorithmic difficulties arise. They are due to the complex shape of the cones including the support of the considered system. These problems can be solved by using an extention of the Newton diagram.
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Submitted on : Tuesday, August 24, 2004 - 4:42:26 PM
Last modification on : Friday, November 6, 2020 - 4:09:34 AM
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  • HAL Id : tel-00006744, version 1



Gérard Eichenmüller. Réduction et intégration symbolique des systèmes d'équations différentielles non-linéaires. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2000. Français. ⟨tel-00006744⟩



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