Formation of a chaotic layer of nonlinear resonance by a two-frequency perturbation

A new effect V. V. Vecheslavov, Zh. éksp. Teor. Fiz. 109, 2208 (1996) (JETP 82, 1190 (1996)]—the appearance of low-frequency secondary harmonics in the separatrix mapping of a system—is discussed in detail for the example of a pendulum with a two-frequency perturbation. It is shown that there exist regions of values of the perturbation parameters where these harmonics make the main contribution to the formation of the chaotic layer of the fundamental resonance. The results of analytical and numerical determinations of the amplitudes of the secondary harmonics are compared. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 989–994 (25 June 1996)