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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.08614
- arXiv:
- arXiv:2012.08614
- Bibcode:
- 2020arXiv201208614A
- Keywords:
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- Physics - Classical Physics;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 12 pages, 2 figures