CHAOTIC DYNAMICS OF QUASI-PERIODICALLY FORCED OSCILLATORS DETECTED BY MELNIKOV METHOD

Nonlinear oscillators that have the form of quasi-periodic perturbations of planar Hamiltonian systems with homoclinic orbits are studied. For such systems, Melnikov's method permits determination, up to the leading term, whether or not the stable and unstable manifolds of normally hyperbolic invariant tori intersect transversely. In a more general setting it is proven that such intersection results in chaotic dynamics. These chaotic orbits are characterized by a generalization of the Bemoulli shift. An example is given to illustrate the theory. The result is also compared with the results of Wiggins [1988b], Scheurle [1986], and Meyer and Sell [1989].