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| HAL : hal-00197145, version 1 |
| arXiv : 0712.2337 |
| Fiche détaillée |  Récupérer au format |
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| Mould expansions for the saddle-node and resurgence monomials |
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| David Sauzin 1 |
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| (14/12/2007) |
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| This article is an introduction to some aspects of 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 or of map. This is illustrated on the case of the saddle-node, a two-dimensional vector field which is 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 is shown to be resurgent in~$1/x$. Resurgence monomials adapted to alien calculus are also described as another application of mould calculus. |
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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 – alien calculus – Stokes phenomenon |
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| hal-00197145, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00197145/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00197145 | |
| Contributeur : David Sauzin | |
| Soumis le : Vendredi 14 Décembre 2007, 13:23:39 | |
| Dernière modification le : Vendredi 14 Décembre 2007, 13:37:04 | |
