Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion

Details Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion

2006-08-07

arxiv.org/abs/math-ph/0608021v2

J. Math. Phys. 48, 012902 (2007) (16 pages)

Physics

Mathematical Physics

31 pages, 8 figures

Scientific paper

10.1063/1.2399359

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.

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