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

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.

31 pages, 8 figures

References in corpus (2)

• Superintegrability with third order invariants in quantum and classical mechanics
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion

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