11 papers
Hamiltonian reduction from particular integrals
R. Azuaje, A. M. Escobar-Ruiz, I. Gutierrez-Sagredo
We develop a geometric reduction mechanism generated by systems of particular integrals, namely, families of functions whose time derivatives close linearly on the family. Their co…
Nonlinear Lissajous orbits and particular superintegrability
A. M. Escobar-Ruiz, R. Azuaje
We investigate the geometry of classical trajectories generated by separable two-dimensional polynomial potentials of the form , wher…
Nodal algebraic curves and entropy diagnostics in degenerate two-dimensional harmonic-oscillator shells
C A Escobar Ruiz, H Olivares-Pilon, A M Escobar-Ruiz
Degenerate quantum eigenspaces can support substantial changes in nodal geometry at fixed energy. We show that, for the two-dimensional isotropic harmonic oscillator, this restruct…
Superintegrability and choreographic obstructions in dihedral -body Hamiltonian systems
A M Escobar-Ruiz, M Fernandez-Guasti
We study planar -body Hamiltonians with quadratic pair interactions whose coupling pattern is invariant under the dihedral group . After the center of mass is removed, the…
On the four-body limaçon choreography: maximal superintegrability and choreographic fragmentation
Adrian M Escobar-Ruiz, Manuel Fernandez-Guasti
In this paper, as a continuation of [Fernandez-Guasti, \textit{Celest Mech Dyn Astron} 137, 4 (2025)], we demonstrate the maximal superintegrability of the reduced Hamiltonian, whi…
Cylindrically confined atom in magnetic field: variational cut-off factor
A. N. Mendoza Tavera, H. Olivares-Pilón, M. RodrÃguez-Arcos +1
In the present study, we consider the hydrogen atom confined within an impenetrable infinite cylindrical cavity of radius in the presence of a constant magnetic field ${\b…