Abstract
We study results on a class of completely integrable systems, for instance, with Hamiltonian H (x,y) = (1/2) 𝒥ni=1y2i +𝒥i<j(xi−yj)−2 +α𝒥ni=1x2i, using quotient manifolds induced by symplectic group actions, which enables us to integrate the systems and understand their complete integrability. In addition, we give a natural interpretation for the scattering maps associated with these systems.
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