Detailed Bifurcations of Periodic Orbits with Threefold Symmetry of the Hénon-Heiles Hamiltonian

Abstract

The bifurcation process of periodic orbits of the Hénon-Heiles Hamiltonian system is investigated by calculating residues. Threefold symmetry of the system induces bifurcations with triple branches, to which the generic bifurcation scheme proposed by Meyer can not be applied. Normal form analysis gives results consistent with numerically observed bifurcations.