Polynomial normal forms with exponentially small remainder for analytic vector fields

Gérard Iooss (1, 2) , Eric Lombardi (3)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 IUF - Institut universitaire de France
3 IF - Institut Fourier

A key tool in the study of the dynamics of vector fields near an equilibrium point is the theory of normal forms, invented by Poincaré, which give simple forms to which a vector field can be reduced close to the equilibrium...

Mots clés: Analytic vector fields; Normal forms; Exponentially small remainders

Domaines: Equations aux dérivées partielles [math.AP]

Gérard Iooss, Eric Lombardi. Polynomial normal forms with exponentially small remainder for analytic vector fields. Journal of Differential Equations, 2005, 212, pp.1-61. ⟨10.1016/j.jde.2004.10.015⟩. ⟨hal-00013597⟩