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Bi-Hamiltonian geometry and canonical spectral coordinates for the Rational Calogero-Moser system

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arxiv 1511.06339 v2 pith:NRGHM25V submitted 2015-11-19 math-ph math.DGmath.MP

Gregorio Falqui , Igor Mencattini This is my paper · ORCID
classification math-phmath.DGmath.MP
keywords coordinatesbi-hamiltoniancalogero-mosercanonicalgeometryrationalspectralsystem
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We reconsider the (rational) Calogero-Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of spectral canonical coordinates, that is, complete sets of Darboux coordinates defined by the eigenvalues and the eigenvectors of the Lax matrix.

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  1. Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models

    math-ph 2019-08 conditional novelty 7.0 of 10

    The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.

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