Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion
Mathematical Physics
2009-11-11 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
We present polynomial Poisson algebras for the 8 classical potentials in two-dimensional Euclidian space that separate in cartesian coordinates and allow a third order integral of motion. Some of the classical superintegrale potentials do not coincide with quantum ones, but are their singular limits. We show that all bounded trajectories in these potentials are periodic.
Keywords
Cite
@article{arxiv.math-ph/0608021,
title = {Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion},
author = {I. Marquette and P. Winternitz},
journal= {arXiv preprint arXiv:math-ph/0608021},
year = {2009}
}
Comments
31 pages, 8 figures