Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

Details Construction of classical superintegrable systems with higher order integrals of motion from ladder operators Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

2010-02-16

arxiv.org/abs/1002.3118v2

J. Math. Phys. 51 7 072903 (2010)

Physics

Mathematical Physics

10 pages, 4 figures, to appear in j.math.phys.

Scientific paper

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.

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