no. 4
Dynamical Systems
Unique normal forms for Hopf-zero vector fields
[Formes normales uniques des champs de vecteurs de type Hopf-zéro]
Présenté par : Bernard Malgrange
Chen, Guoting1 ; Wang, Duo2 ; Yang, Jiazhong2
1 UFR de mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq, France
2 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
Comptes Rendus. Mathématique, Tome 336 (2003) no. 4, pp. 345-348

We consider normal forms of Hopf-zero vector fields in R 3 . Unique normal forms under conjugacy and orbital equivalence for the generic case are given.

Nous étudions l'unicité des formes normales de champs de vecteurs de type Hopf-zéro dans R 3 . Des formes normales uniques dans le cas générique sont données par rapport aux changements de coordonnées et pour l'équivalence orbitale.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00043-8

Chen, Guoting 1 ; Wang, Duo 2 ; Yang, Jiazhong 2

1 UFR de mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq, France
2 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China 
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Chen, Guoting; Wang, Duo; Yang, Jiazhong. Unique normal forms for Hopf-zero vector fields. Comptes Rendus. Mathématique, Tome 336 (2003) no. 4, pp. 345-348. doi: 10.1016/S1631-073X(03)00043-8

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[3] Ichikawa, F. On finite determinacy of formal vector fields, Invent. Math., Volume 70 (1982), pp. 45-52

[4] Kokubu, H.; Oka, H.; Wang, D. Linear grading function and further reduction of normal forms, J. Differential Equations, Volume 132 (1996), pp. 293-318

[5] J. Lamb, M.A. Teixeira, J. Yang, On the Hamiltonian structure of normal forms for elliptic equilibria of reversible vector fields in R 4 , Preprint, 2002

[6] Yu, P.; Yuan, Y. The simplest normal form for the singularity of a pure imaginary and a zero eigenvalue, Dyn. Cont. Disc. Impul. Syst. Ser. B, Appl. and Algorithms, Volume 8 (2001), pp. 219-249

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