3813 サドル・センターを有する多自由度ハミルトン系の非可積分性

Abstract

We consider a class of three or more degrees of freedom Hamiltonian systems which have saddle-centers with homoclinic orbits. Using a Melnikov-type global perturbation technique, we obtain a condition under which transverse homoclinic and heteroclinic orbits to invariant tori consisting of quasiperiodic orbits near the saddle-centers exist. The presence of such orbits means the nonintegrability of the Hamiltonian systems and the occurrence of chaos and Arnold diffusion type behavior. We apply the theory to systems with potentials and give a concrete example.