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We reconsider the (rational) Calogero-Moser system from the point of view ofbi-Hamiltonian geometry. By using geometrical tools of the latter, weexplicitly construct set(s) of spectral canonical coordinates, that is,complete sets of Darboux coordinates defined by the eigenvalues and theeigenvectors of the Lax matrix.

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