We present general results pertaining to chaotic motions in a class of systems termed slowly varying oscillators which consist of weakly perturbed single-degree-of-freedom systems in which parameters vary slowly in time according to an additional equation of motion. Our results include an analytical method for detecting transversal intersections of stable and unstable manifolds (typically a necessary condition for chaotic motions to exist) and a detailed description of the chaotic dynamics that occur when this situation exists.

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