Connecting orbits for families of Tonelli Hamiltonians
Résumé
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].