2D-Generating Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – II

In earlier research, we developed two techniques designed to expand the construction of a periodic orbit dividing surface for Hamiltonian systems with three or more degrees of freedom. Our methodology involved transforming a periodic orbit into a torus or cylinder, thereby elevating it to a higher-dimensional structure within the energy surface (refer to [ Katsanikas & Wiggins , 2021a , 2021b , 2023a , 2023b ]). Recently, we introduced two new methods for creating dividing surfaces, which do not rely on periodic orbits. Instead, we used 2D surfaces (geometric entities) or 3D surfaces in a Hamiltonian system with three degrees of freedom (see [ Katsanikas & Wiggins , 2024a , 2024b , 2024c ]). In these studies, we applied these surfaces within a quadratic normal-form Hamiltonian system with three degrees of freedom. This series of two papers (this paper and [ Katsanikas et al. , 2024 ]) extends our results to 2D-generating surfaces for quartic Hamiltonian systems with three degrees of freedom. This paper focuses on presenting the second method of constructing 2D-generating surfaces.