 |
|
|
|
| HAL : hal-00201446, version 2 |
| arXiv : 0801.0073 |
| Fiche détaillée |  Récupérer au format |
|
|
| Versions disponibles : | v1 (29-12-2007) | v2 (12-01-2008) |
|
|
|
|
| Initiation to mould calculus through the example of saddle-node singularities |
|
|
| David Sauzin 1 |
|
|
| (28/12/2007) |
|
|
|
| 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~$1/x$. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE) |
|
|
|
CNRS : UMR8028 – INSU – Observatoire de Paris – Université Paris VI - Pierre et Marie Curie – Université Lille 1 - Sciences et Technologies |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Systèmes dynamiques |
|
|
| Resurgence theory – mould calculus – saddle-node |
|
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00201446, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00201446 | |
| 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 | |
