Chaotische Bewegung auf Hamiltonschen Tori

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. We show that certain Hamiltonian systems contain invariant nonregular tori with compressible flow. Using as an example an electron moving in electromagnetic fields which are periodic in space we demonstrate (i) that strange attractors (and repellets) of well-known autonomous or (quasi-)periodically time-driven systems may occur on such strange tori, (ii) that one may find barriers consisting of nonregular 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-Lori transform into nonregular tori - rather than breaking np - when the perturbation becomes strong