Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation
In this paper the authors give a new global perturbation technique, fundamentally different from others, for detecting homoclinic and heteroclinic orbits in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two-degree-of- freedom Hamiltonian systems. By this technique, the orbits homoclinic and heteroclinic to fixed points that are created in a resonance resulting from the perturbation are determined, and the conditions under which these homoclinic connections can lead to chaotic dynamics are discussed, and an application to a modified model of the forced and damped sine- Gordon equation developed by Bishop et al. is given.
scientific article; zbMATH DE number 91642
scientific article