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arXiv · 0910.0299

Periodic orbits for an infinite family of classical superintegrable systems

Frédérick Tremblay·Alexander V. Turbiner·Pavel Winternitz
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Abstract

We show that all bounded trajectories in the two dimensional classical system with the potential $V(r,ϕ)=ω^2 r^2+ \frac{\al k^2}{r^2 \cos^2 {k ϕ}}+ \frac{βk^2}{r^2 \sin^2 {k ϕ}}$ are closed for all integer and rational values of $k$. The period is $T=\fracπ{2ω}$ and does not depend on $k$. This agrees with our earlier conjecture suggesting that the quantum version of this system is superintegrable.

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Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz. 2009-10-02. Periodic orbits for an infinite family of classical superintegrable systems. https://doi.org/10.1088/1751-8113%2F43%2F1%2F015202

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