Resonance seeding of stability boundaries in two and four dimensions

摘要

''Resonance seeding'' refers to the hypothesis that the stochastic layer delineating the dynamic aperture of a Hamiltonian system grows out of separatrices generated by a very low order resonances. This is a physics hypothesis and should not be interpreted as arising from any particular technique for writing perturbative expansions, such as the ones developed by Deprit, Dragt, or Forest. Although analytic representations of the resonances are indeed obtained via perturbation theory, existence of the separatrices and the validity (or otherwise) for resonance seeding are separate from it. We shall describe some of the evidence supporting this idea in two and four dimensions.