Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems - Université de Rennes Accéder directement au contenu
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2016

Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems

Résumé

In this paper we study the dynamics near the equilibrium point of a family of Hamiltonian systems in the neighborhood of a $0^2i\omega$ resonance. The existence of a family of periodic orbits surrounding the equilibrium is well-known and we show here the existence of homoclinic connections with several loops for every periodic orbit close to the origin, except the origin itself. The same problem was studied before for reversible non Hamiltonian vector fields, and the splitting of the homoclinic orbits lead to exponentially small terms which prevent the existence of homoclinic connections with one loop to exponentially small periodic orbits. The same phenomenon occurs here but we get round this difficulty thanks to geometric arguments specific to Hamiltonian systems and by studying homoclinic orbits with many loops.
Fichier principal
Vignette du fichier
Article2_12.pdf (1.48 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01251087 , version 1 (05-01-2016)

Identifiants

Citer

Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete and Continuous Dynamical Systems - Series A, 2016, 36 (6), pp.3153-3225. ⟨10.3934/dcds.2016.36.xx⟩. ⟨hal-01251087⟩
449 Consultations
157 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More