Chaotic motion on Hamiltonian tori

Abstract

KAM tori are well known to be that (finite!) part of phase space in which the motion of a weakly perturbed classical Hamiltonian system remains integrable. Moreover, they are barriers in the phase space of systems with two degrees of freedom. The authors show that certain Hamiltonian systems contain invariant non-regular tori with compressible flow. Using as an example an electron moving in electromagnetic fields which are periodic in space they demonstrate: (i) that strange attractors (and repellers) of well known autonomous or (quasi-)periodically time-driven systems may occur on such strange tori; (ii) that one may find barriers consisting of non-regular Hamiltonian tori in systems with any number of degrees of freedom (the flow on such barriers is non-chaotic, though); and (iii) that certain KAM tori transform into non-regular tori-rather than breaking up-when the perturbation becomes strong.