Bifurcations into pathology for Hamiltonian systems
A two degrees of freedom potential (Hamiltonian) system is considered where the origin is a non-degenerate local maximum. The total energy level is considered as a bifurcation parameter. In the example treated periodic orbits bifurcate at a certain energy level through simultaneous homoclinic bifurcations. Introducing a second bifurcation parameter a still higher pathology occurs at a critical value.
scientific article; zbMATH DE number 4063571