The chaotic layer of a nonlinear resonance under low-frequency perturbation

Conditions whereby the chaotic layer of a nonlinear resonance is described in terms of low-frequency separatrix mapping are discussed. In this case, the accurate estimation of the size of the layer requires the arrangement of resonances at its edge to be known. The resonance picture is constructed using the separatrix mapping invariants of the first three orders. The variation of the layer size with the mapping amplitude is traced with the criterion for resonance overlapping. Results obtained by direct calculation and by invariants analysis are compared. Issues that remain to be solved are noted.