Bifurcation of periodic orbits near a frequency maximum in near- integrable driven oscillators with friction
(From authors' abstract.) The authors investigate analytically the effect of perturbations on an integrable oscillator with one degree of freedom whose frequency shows a maximum as a function of the energy, i.e. a system with nonmonotone twist. The perturbation depends on three parameters: friction, variation of the frequency, strength of the driving force. The main result is the appearance of two chains of saddle node pairs in the phase portrait. This contrasts with the bifurcation of one chain of periodic orbits in the case of perturbations of monotone twist systems. The result is obtained for a mapping, but it is demonstrated that the same formalism and results apply for time continuous systems as well.
scientific article; zbMATH DE number 168466