Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials

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 $\tilde{a}$ 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.

arXiv comment12 pages, 2 figures

References in corpus (10)

• Third order superintegrable systems separating in polar coordinates
• Universal charge and current on magnetic domain walls in Weyl semimetals
• The anisotropic oscillator on curved spaces: A new exactly solvable model
• Commensurate Harmonic Oscillators: Classical Symmetries
• The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• General $N^{th}$-order superintegrable systems separating in polar coordinates
• Superintegrable systems on spaces of constant curvature
• An exact solution of the Dirac equation with CP violation
• Lobachevsky geometry in TTW and PW systems