Normal forms with exponentially small remainder: application to homoclinic connections for the reversible 02+i? resonance

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

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 IF - Institut Fourier

In this Note we explain how the normal form theorem already established (Iooss and Lombardi, J. Differential Equations, in press) for analytic vector fields with a semi-simple linearization enables to prove the existence of homoclinic connections to exponentially small periodic orbits for reversible analytic vector fields admitting a 02+i? resonance where the linearization is precisely not semi simple.

Mots clés: Ordinary Differential Equations/Dynamical Systems

Domaines: Systèmes dynamiques [math.DS]

Gérard Iooss, Eric Lombardi. Normal forms with exponentially small remainder: application to homoclinic connections for the reversible 02+i? resonance. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339 (12), pp.831-838. ⟨10.1016/j.crma.2004.10.00⟩. ⟨hal-00014723⟩