The Kepler problem: polynomial algebra of non-polynomial first integrals
Exactly Solvable and Integrable Systems
2019-09-04 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors is defined by a fixed point on the curve. Algebra of the first integrals associated with symmetries is a well-known mathematical object, whereas algebra of the first integrals associated with coordinates of fixed points is unknown. In this paper, we discuss polynomial algebras of non-polynomial first integrals of superintegrable systems associated with elliptic curves.
Cite
@article{arxiv.1903.08846,
title = {The Kepler problem: polynomial algebra of non-polynomial first integrals},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:1903.08846},
year = {2019}
}
Comments
LaTex with AMS fonts, 18 pages