Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials
Classical Physics
2020-12-17 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
A Hamiltonian dynamics defined on the two-dimensional hyperbolic plane by coupling the Morse and Rosen-Morse potentials is analyzed. It is demonstrated that orbits of all bounded motions are closed iff the product of the parameter of the Morse potential and the square root of the absolute value of the curvature is a rational number. This property of trajectories equivalent to the maximal superintegrability is confirmed by explicit construction of polynomial superconstant of motion.
Cite
@article{arxiv.2012.08614,
title = {Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials},
author = {John Acosta and Cezary Gonera},
journal= {arXiv preprint arXiv:2012.08614},
year = {2020}
}
Comments
12 pages, 2 figures