MATCHING ACROSS SUBHARMONIC RESONANCES

A strongly nonlinear oscillator is analyzed with an O(epsilon) dissipa tive perturbation and an O(epsilon) periodic forcing. Multiphase avera ging determines the modulations of the energy and phase, but is known to fail near subharmonic resonance layers. We include an O(epsilon) ju mp in the energy across each subharmonic resonant layer which is neede d to determine the phase after resonance. This is in addition to the u sual O(epsilon(1/2)) jump in energy determined by the method of matche d asymptotic expansions. We introduce a time shift for the energy afte r subharmonic resonance which is equivalent to the jump in energy. We show that the phase after a subharmonic resonance is described by the same time shift if an elementary phase adjustment is made.