Isochronous and period doubling bifurcations of periodic solutions of non-integrable Hamiltonian systems with reflexion symmetries

Abstract

We analytically derive the possible types of isochronous and period doubling bifurcations undergone by periodic solutions of two degrees of freedom, non-integrable, Hamiltonian systems possessing reflexion and time-reversal symmetries. We find that one of the isochronous bifurcations numerically found in refs. [3] cannot exist. In the case of period-doubling we predict the existence of a type of bifurcation not found in refs. [2] and [3] but confirmed by further numerical investigation.