Divergence and summability of normal forms of systems of differential equations with nilpotent linear part

@article{CanalisDurand2004DivergenceAS,
  title={Divergence and summability of normal forms of systems of differential equations with nilpotent linear part},
  author={Mireille Canalis-Durand and Reinhard Sch{\"a}fke},
  journal={Annales de la Facult{\'e} des Sciences de Toulouse},
  year={2004},
  volume={13},
  pages={493-513}
}
On considere des formes prenormales associees a des perturbations generiques du systeme x = 2y, y = 3x 2 . Il est connu qu'elles admettent une forme normale formelle x = 2y+2xΔ*, y = 3x 2 +3yΔ*, ou Δ* = A 0 (h)+xA 1 (h) avec h = y 2 - x 3 ([Loray, 1999]). Nous demontrons que A 0 , A 1 et les transformations normalisantes sont divergentes, mais k-sommables. L'entier k depend des premiers termes non nuls de A 0 et A 1 . 

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