PERIODIC-SOLUTIONS OF A SYSTEM OF COUPLED OSCILLATORS NEAR RESONANCE

A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbol ic but is normally nondegenerate. The bifurcation function whose zeros are the bifurcation points for families of perturbed periodic solutio ns is determined. This result is applied to find the periodic solution s near resonance for a two-degrees-of-freedom mechanical system modeli ng a rotor interacting with an elastic support.