An asymptotic solution to a problem involving two simultaneous small divisors

This paper concerns a model problem illustrating the techniques needed to analyze weakly nonlinear oscillator systems wherein two small divisors (resonances) may occur separately or simultaneously. The method of multiple scales in combination with singular perturbation methods is used to construct a uniformly valid asymptotic solution to the proposed model equation. It is shown that matching is necessary in order to establish a composite solution uniformly valid for the entire phase plane. The model equation does not encompass the class of problems where occurrence of two simultaneous small divisors leads to Kolmogorov-Arnol'd-Moser amplitude instability.This work was supported in part by the National Science Foundation under NSF Grant Number GP-32030.