Oscillations near separatrix for perturbed Duffing equation
arXiv:0903.4523
Abstract
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution is defined by a separatrix map. This map is obtained for any order of the perturbation parameter. Properties of this map show an instability of a motion for the perturbed system.
17 pages, 4 figures