We present a plethora of homoclinic and heteroclinic orbits that exist in the phase space of a weakly nonlinear model describing small oscillations of two resonantly driven coupled pendula. These orbits connect equilibria in a resonance band, which is contained in an invariant plane, and is born under perturbation out of a circle of equilibria. Their existence is shown by using a combination of the Melnikov method and singular perturbation techniques.

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This work was partly supported by the U.S. Department of Energy through grant DE-FG02-93ER25154, and the National Science Foundation through grants DMS-9403750 and DMS-9502142.

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