Multiple separatrix crossing: A chaos structure

Numerical experiments on the structure of the chaotic component of motion under multiple-crossing of the separatrix of a nonlinear resonance with a time-varying amplitude are described with the emphasis on the ergodicity problem. The results clearly demonstrate nonergodicity of this motion due to the presence of a regular component of a relatively small measure with a very complicated structure. A simple 2D-map per crossing is constructed that qualitatively describes the main properties of both chaotic and regular components of the motion. An empirical relation for the correlation-affected diffusion rate is found including a close vicinity of the chaos border where evidence of the critical structure is observed. Some unsolved problems and open questions are also discussed. (C) 2000 MAIK "Nauka/Interperiodica".