Connecting orbits for families of Tonelli Hamiltonians

Vito Mandorino (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the flows of a family of Tonelli Hamiltonians. Our approach is close to the one of Bernard in [3]. When specialized to families of twist maps, our results are similar to those of Moeckel [20] and Le Calvez [15], and generalize the connecting results of Mather for a single twist map in [18].

Mots clés: Arnold diffusion; Tonelli Hamiltonian; polysystem; connecting orbits; weak KAM theory; Lax-Oleinik operator

Domaines: Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]

Vito Mandorino. Connecting orbits for families of Tonelli Hamiltonians. Journal of modern dynamics, 2012, 6 (4), pp.499-538. ⟨10.3934/jmd.2012.6.499⟩. ⟨hal-00617367⟩