RESONANT LAYERS IN NONLINEAR DYNAMICS

A new method based on an incremental energy approach and the standard mapping technique is proposed for the study of resonant layers in nonl inear dynamics. To demonstrate the procedure, the method is applied to four types of Duffing oscillators. The appearance, disappearance and accumulated disappearance strengths of the resonant layers for each ty pe of oscillator are derived. A quantitative check of the appearance s trength is performed by computing its value using three independent me thods: Chirikov overlap criterion, renormalization group technique, an d numerical simulations. It is also observed that for the case of the twin-well Duffing oscillator, its perturbed left and right wells are a symmetric.