3D Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – II

In our previous studies [ Katsanikas & Wiggins , 2021a , 2021b , 2023a , 2023b , 2024a , 2024b , 2024c ], we presented two methods for building up dividing surfaces based on either periodic orbits or 2D/3D generating surfaces, specifically for Hamiltonian systems with three or more degrees of freedom. These papers extended these dividing surface constructions to allow for more complex forms, such as tori or cylinders, embedded within the energy surface of the Hamiltonian system. These studies were applied to a quadratic normal form Hamiltonian system with three degrees of freedom. This series of papers extends our findings to 3D generating surfaces for three degrees of freedom quartic Hamiltonian systems. This paper focuses on the second approach for constructing these 3D generating surfaces.