Elliptic curve arithmetic and superintegrable systems
Exactly Solvable and Integrable Systems
2019-05-22 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
Harmonic oscillator and the Kepler problem are superintegrable systems which admit more integrals of motion than degrees of freedom and all these integrals are polynomials in momenta. We present superintegrable deformations of the oscillator and the Kepler problem with algebraic and rational first integrals. Also, we discuss a family of superintegrable metrics on the two-dimensional sphere, which have similar first integrals.
Cite
@article{arxiv.1810.11991,
title = {Elliptic curve arithmetic and superintegrable systems},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:1810.11991},
year = {2019}
}
Comments
17 pages, 3 figures, LaTeX with Amsfonts, with corrected misprints