Abstract
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.
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 122, No. 1, 2002, pp. 175–187.
Original Russian Text Copyright © 2002 by Vecheslavov, Chirikov.
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Vecheslavov, V.V., Chirikov, B.V. Diffusion in smooth Hamiltonian systems. J. Exp. Theor. Phys. 95, 154–165 (2002). https://doi.org/10.1134/1.1499913
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DOI: https://doi.org/10.1134/1.1499913