On a mechanism of diffusion in Hamiltonian systems

The mechanism of diffusion in Hamiltonian systems close to completely integrable is usually associated with the existence of so-called “transition chains”: slow diffusion takes place in a neighborhood of intersecting separatrices of hyperbolic periodic solutions (or, more generally, low-dimensional invariant tori) of the perturbed problem. In the paper we discuss another diffusion mechanism which is based on the destruction of almost resonant invariant tori of an unperturbed system. This mechanism is illustrated by the example of an isoenergically non-degenerate Hamiltonian system with three degrees of freedom. However, similar behaviour can take place in general multidimensional Hamiltonian systems. The proof of the presence of drift of slow variables is based on the analysis of integrals of quasiperiodic functions of time with zero mean value (these integrals can be unlimited), and also uses the conditions of topological transitivity of cylindrical cascades.