ЖЭТФ, Том 117,
стр. 1030 (Май 2000)
(Английский перевод - JETP,
Vol. 90, No 5,
доступен on-line на www.springer.com
MULTIPLE SEPARATRIX CROSSING: A CHAOS STRUCTURE
Chirikov B.V., Vecheslavov V.V.
Поступила в редакцию: 20 Января 2000
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 an evidence of the critical structure is observed. Some unsolved problems and open questions are also discussed.