Diffusion in smooth Hamiltonian systems

A family of models determined by a smooth canonical 2D-map that depends on two parameters is studied. Preliminary results of numerical experiments are reported; they are evidence of substantial suppression of global diffusion in a wide range of perturbation values. This effect is caused by the little-known phenomenon of the conservation of resonance separatrices and other invariant curves under the conditions of strong local dynamic chaos. Such a total suppression of diffusion occurs although invariant curves are only conserved for a countable zero-measure set of parameter values. Simple refined estimates of diffusion rates in smooth systems without invariant curves were obtained and numerically substantiated. The principal boundary of diffusion suppression in a family of models with invariant curves was described by a semiempirical equation in dimensionless variables. The results were subjected to a statistical analysis, and an integral distribution for diffusion suppression probability was obtained.