Fine structure of splitting of the separatrix of a nonlinear resonance

This report is a continuation of an analysis, initiated elsewhere V.V. Vecheslavov and B. V. Chirikov, Zh. Éksp. Teor. Fiz. 114, 1516 (1998) [JETP 86, 823 (1998)], of the effect of splitting of the separatrix of a nonlinear resonance for the model of standard mapping, based on results of direct measurements of the splitting angle α(K), where K is the system parameter. Measurements were made in the previously used wide range 0.1≳α≳10−208 (1⩾K⩾0.0004), but with significantly higher relative (better than 1050) and average (∼10−55) accuracy. This procedure made it possible to substantially refine the effects observed in Ref. 1 and construct qualitatively new empirical dependences providing reliable extrapolation of the data obtained for the angle and the invariant in the intermediate asymptotic limit K≲10−2 beyond the limits of the investigated region. The results obtained by us can be useful for further development of the theory of separatrix splitting and formation of the stochastic layer of a nonlinear resonance.