Intersecting resonances and chaos in a three-oscillator model. I. Classical studies

We consider a model system of three weakly coupled, weakly anharmonic oscillators, containing two near 2:1 Fermi resonances. This system is initially reduced via a resonance approximation to one of two coupled pendula, each pendulum representing one of the interoscillator resonances. This leads to a natural description of the system in terms of analytically predictable resonance zones and their intersection in action space. A full numerical analysis of the classical dynamics of the two-pendulum system is given, with respect to both the appearance of stochasticity and the development of periodic orbits in the resulting two-dimensional area-preserving map. The success of the resonance approximation in describing adequately the behavior of the three-oscillator model is shown by comparison with a representative study of the classical dynamics of the full three-oscillator model.