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Obstruction à la linéarisation des champs de vecteurs polynomiaux

  • Jacky Cresson (a1)
Résumé

On explicite une classe de champ de vecteurs polynomiaux non analytiquement lin éarisables à l'aide de la correction introduite par Écalle-Vallet. Notamment, on étend des résultats de Schuman sur la trivialit é des hamiltoniens homogàenes isochrones.

Abstract

We characterize a class of polynomial vector fields which are not analytically linearizable using the correction introduced by Écalle-Vallet. Then, we extend Schuman's result about non existence of isochronous homogenous Hamiltonian systems.

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References
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[1] Cresson, J. et Schuman, B., Formes normales et probléeme du centre. Bull. Sci. Math. (3) 125 (2001), 1252001.
[2] Cresson, J. et Schuman, B., Formes normales et probléeme du centre symétrique. C. R. Acad. Sci. Paris Sér. I 327 (1998), 3271998.
[3] Cresson, J., Calcul moulien (avec un avant propos de Jean Écalle). á paraître dans les Actes du colloque, Polylogarithmes et conjectures de Deligne-Ihara, (Luminy), C.I.R.M., avril 2000.
[4] Écalle, J. et Vallet, B., Correction and linearization of resonant vector fields and diffeomorphisms. Math. Z., 229 (1998), 2291998.
[5] Françoise, J.-P. et Pons, R., Computer algebra methods and the stability of differential systems. Random and Computational Dynamics (4) 3 (1995), 31995.
[6] Schuman, B., Sur la forme normale de Birkhoff et les centres isochrones. C. R. Acad. Sci. Paris S ér. I 322 (1996), 3221996.
[7] Schuman, B., Une classe d'hamiltoniens isochrones. prépublication 168, Mai 1998, Institut de Mathématiques de Jussieu, á paraître á Canad. J. Math.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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