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Superintegrable Calogero-type systems admit maximal number of Poisson structures

C. Gonera·Y. Nutku
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Abstract

We present a general scheme for constructing the Poisson structure of super-integrable dynamical systems of which the rational Calogero-Moser system is one of the most interesting one. This dynamical system is $2N$ dimensional with $2N- 1$ first integrals and our construction yields $2N-1$ degenerate Poisson tensors that each admit $2(N-1)$ Casimirs. Our results are quite generally applicable to all super-integrable systems and form an alternative to the traditional bi-Hamiltonian approach.

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C. Gonera, Y. Nutku. 2001-05-24. Superintegrable Calogero-type systems admit maximal number of Poisson structures. https://doi.org/10.1016/s0375-9601(01)00365-6

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