Multidimensional Hamiltonian chaos

In Hamiltonian systems that are close to nondegenerate integrable systems, Arnold diffusion does not arise in the case of two degrees of freedom; for a larger number of degrees of freedom the diffusion is, generally speaking, exponentially slow. If a nonperturbed system is degenerate, diffusion proceeding according to a stochastic pattern may arise even with two degrees of freedom. It is shown that in this case the introduction of additional degrees of freedom may lead to a sharp increase in the diffusion rate and in the measure of the phase space chaotic component due to the destruction of the stochastic pattern. The results pertain to the 2 1/2 degree of freedom problem of the motion of a charged particle in a magnetic field or in the field of a wave packet propagating at an angle with respect to the magnetic field.