47 citations · 608 across the 32 of their papers we have counts for
25 papers · 1 filter
The evolution of the phase space structure along pitchfork and period-doubling bifurcations in a 3D galactic bar potential
Henok Tenaw Moges, Matthaios Katsanikas, Panos Patsis +2
We investigate how the phase space structure of a 3D autonomous Hamiltonian system evolves across a series of successive 2D and 3D pitchfork and period-doubling bifurcations, as th…
Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the…
Phase space transport in a symmetric Caldera potential with three index-1 saddles and no minima
M. Katsanikas, M. Agaoglou, S. Wiggins +1
We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that c…
The Nature of Reactive and Non-reactive Trajectories for a Three Dimensional Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of the…
The time evolution of the trajectories after the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation
Douglas Haigh, Matthaios Katsanikas, Makrina Agaoglou +1
Selectivity is an important phenomenon in chemical reaction dynamics. This can be quantified by the branching ratio of the trajectories that visit one or the other wells to the tot…
Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation
Matthaios Katsanikas, Makrina Agaoglou, Stephen Wiggins
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. T…
The Generalization of the Periodic Orbit Dividing Surface in Hamiltonian Systems with three or more degrees of freedom -- I
M. Katsanikas, S. Wiggins
We present a method that generalizes the periodic orbit dividing surface construction for Hamiltonian systems with three or more degrees of freedom. We construct a torus using as a…
Bifurcation Study on a Degenerate Double van der Waals Cirque Potential Energy Surface using Lagrangian Descriptors
M. Katsanikas, B. Aguilar Sanjuan, F. Gonzalez Montoya +2
In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is inc…
The bifurcations of the critical points and the role of the depth in a symmetric Caldera potential energy surface
Y. Geng, M. Katsanikas, M. Agaoglou +1
In this work, we continue the study of the bifurcations of the critical points in a symmetric Caldera potential energy surface. In particular, we study the influence of the depth o…
Visualizing the Phase Space of the HeI_2 van der Waals Complex using Lagrangian Descriptors
M. Agaoglou, V. J. Garcia-Garrido, M. Katsanikas +1
In this paper we demonstrate the capability of the method of Lagrangian descriptors to unveil the phase space structures that characterize transport in high-dimensional symplectic…
Revealing the phase space structure of Hamiltonian systems using the action
Francisco Gonzalez Montoya, Makrina Agaoglou, Matthaios Katsanikas
In this work, we analyse the properties of the Maupertuis' action as a tool to reveal the phase space structure for Hamiltonian systems. We construct a scalar field with the action…
From Poincare Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential
R. Crossley, M. Agaoglou, M. Katsanikas +1
In this paper we compare the method of Lagrangian descriptors with the classical method of Poincare maps for revealing the phase space structure of two degree-of-freedom Hamiltonia…
The Influence of a Pitchfork Bifurcation of the Critical Points of a Symmetric Caldera Potential Energy Surface on Dynamical Matching
Y. Geng, M. Katsanikas, M. Agaoglou +1
Many organic chemical reactions are governed by potential energy surfaces that have a region with the topographical features of a caldera. If the caldera has a symmetry then trajec…
Phase Space Analysis of the Dynamics on a Potential Energy Surface with an Entrance Channel and Two Potential Wells
M. Katsanikas, V. J. García-Garrido, M. Agaoglou +1
In this paper we unveil the geometrical template of phase space structures that governs transport in a Hamiltonian system described by a potential energy surface with an entrance/e…
Detection of Dynamical Matching in a Caldera Hamiltonian System using Lagrangian Descriptors
M. Katsanikas, Víctor J. García-Garrido, S. Wiggins
The goal of this paper is to apply the method of Lagrangian descriptors to reveal the phase space mechanism by which a Caldera-type potential energy surface (PES) exhibits the dyna…
Phase Space Analysis of the Non-Existence of Dynamical Matching in a Stretched Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
In this paper we continue our studies of the two dimensional caldera potential energy surface in a parametrized family that allows for a study of the effect of symmetry on the phas…
Phase Space Structure and Transport in a Caldera Potential Energy Surface
Matthaios Katsanikas, Stephen Wiggins
We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow…
The phase-space of boxy-peanut and X-shaped bulges in galaxies I. Properties of non-periodic orbits
P. A. Patsis, M. Katsanikas
The investigation of the phase-space properties of structures encountered in a dynamical system is essential for understanding their formation and enhancement. In the present paper…
Analytical study of the structure of chaos near unstable points
G. Contopoulos, C. Efthymiopoulos, M. Katsanikas
In a 2D conservative Hamiltonian system there is a formal integral besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unsta…
Analytical invariant manifolds near unstable points and the structure of chaos
C. Efthymiopoulos, G. Contopoulos, M. Katsanikas
It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958…
The structure of phase space close to fixed points in a 4D symplectic map
L. Zachilas, M. Katsanikas, P. A. Patsis
We study the dynamics in the neighborhood of fixed points in a 4D symplectic map by means of the color and rotation method. We compare the results with the corresponding cases enco…
Instabilities and stickiness in a 3D rotating galactic potential
M. Katsanikas, P. A. Patsis, G. Contopoulos
We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the f…
Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential
M. Katsanikas, P. A. Patsis, A. D. Pinotsis
This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential o…
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
M. Katsanikas, P. A. Patsis, G. Contopoulos
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodi…