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| HAL : hal-00201446, version 2 |
| arXiv : 0801.0073 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (29-12-2007) | v2 (12-01-2008) |
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| Initiation to mould calculus through the example of saddle-node singularities |
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| David Sauzin 1 |
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| (28/12/2007) |
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| This article proposes an initiation to Écalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is illustrated on the case of saddle-node singularities, generated by two-dimensional vector fields which are formally conjugate to Euler's vector field $x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal normalisation proves to be resurgent in~$1/x$. |
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| 1 : | Institut de Mecanique Celeste et de Calcul des Ephemerides (IMCCE) |
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CNRS : UMR8028 – INSU – Observatoire de Paris – Université Pierre et Marie Curie - Paris VI |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Resurgence theory – mould calculus – saddle-node |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00201446, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00201446/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00201446 | |
| Contributeur : David Sauzin | |
| Soumis le : Samedi 12 Janvier 2008, 10:16:16 | |
| Dernière modification le : Samedi 12 Janvier 2008, 12:45:24 | |
