Abstract
We present the numerical and analytical evidences are given of the fact that the formation of a chaotic layer of a nonlinear resonance under the action of multifrequency perturbation is qualitatively different from the case of a single-frequency perturbation which is well studied by now. The new effect of appearance in the separatrix mapping of the system of low-frequency secondary harmonics is discussed and the conditions under which just these harmonics play the dominant role in the formation of chaos are found. Theoretical estimates of the secondary harmonic amplitudes are compared with the results of numerical calculations. Invariants of the first two orders of separatrix mapping enabling one to produce an approximate picture of resonance overlapping on the edge of the chaotic layer and to get its size value are introduced.
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