Normal forms with exponentially small remainder : application to homoclinic connections for the reversible 0 2+ iω resonance

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

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IUF - Institut universitaire de France
3 IMT - Institut de Mathématiques de Toulouse UMR5219

In this note we explain how the normal form theorem established in [2] 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 0 2+ iω resonance where the linearization is precisely not semi simple.

Domaines: Systèmes dynamiques [math.DS]; Formation de Structures et Solitons [nlin.PS]; Equations aux dérivées partielles [math.AP]

Gérard Iooss, Eric Lombardi. Normal forms with exponentially small remainder : application to homoclinic connections for the reversible 0 2+ iω resonance. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339, pp.8. ⟨hal-01265190⟩