3D generating surfaces in Hamiltonian systems with three degrees of freedom–I

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2024 - World Scientific
In our earlier research (see [Katsanikas & Wiggins,,,,,]), we developed two methods for
creating dividing surfaces, either based on periodic orbits or two-dimensional generating …

2D generating surfaces and dividing surfaces in Hamiltonian systems with three degrees of freedom

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2024 - World Scientific
In our previous work, we developed two methods for generalizing the construction of a
periodic orbit dividing surface for a Hamiltonian system with three or more degrees of …

3D generating surfaces in Hamiltonian systems with three degrees of freedom–II

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2024 - World Scientific
Our paper is a continuation of a previous work referenced as [Katsanikas & Wiggins,]. In this
new paper, we present a second method for computing three-dimensional generating …

The influence of asymmetry on the dynamics associated with a Caldera potential energy surface

M Katsanikas, M Hillebrand, C Skokos… - International Journal of …, 2022 - World Scientific
In this paper, we analyze the influence of asymmetry on a Caldera potential energy surface.
We first study the effect of asymmetry on the structure of the periodic orbit dividing surfaces …

Periodic orbit dividing surfaces in a quartic Hamiltonian system with three degrees of freedom–I

F Gonzalez Montoya, M Katsanikas… - International Journal of …, 2024 - World Scientific
In prior work [Katsanikas & Wiggins, 2021a, 2021b, 2023c, 2023d], we introduced two
methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored for …

The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom-III

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2023 - World Scientific
In two previous papers [Katsanikas & Wiggins, 2021a, 2021b], we developed two methods
for the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or …

2D generating surfaces in a quartic Hamiltonian system with three degrees of freedom–I

M Katsanikas, F Gonzalez Montoya… - International Journal of …, 2024 - World Scientific
In previous studies, we developed two techniques aimed at expanding the scope of
constructing a periodic orbit dividing surface within a Hamiltonian system with three or more …

The generalization of the periodic orbit dividing surface for Hamiltonian systems with three or more degrees of freedom–IV

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2023 - World Scientific
Recently, we presented two methods of constructing periodic orbit dividing surfaces for
Hamiltonian systems with three or more degrees of freedom [Katsanikas & Wiggins, 2021a …

Periodic Orbit-Dividing Surfaces in Rotating Hamiltonian Systems with Three Degrees of Freedom–I

M Katsanikas, S Wiggins - International Journal of Bifurcation and …, 2024 - World Scientific
In this paper, we extend the notion of periodic orbit-dividing surfaces (PODSs) to rotating
Hamiltonian systems with three degrees of freedom. First, we present how to apply our first …

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

M Katsanikas, FG Montoya, S Wiggins - International Journal of …, 2024 - World Scientific
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 …