Communications in Mathematical Physics

, Volume 115, Issue 1, pp 127–165

Action-angle maps and scattering theory for some finite-dimensional integrable systems

I. The pure soliton case


  • S. N. M. Ruijsenaars
    • Centre for Mathematics and Computer Science

DOI: 10.1007/BF01238855

Cite this article as:
Ruijsenaars, S.N.M. Commun.Math. Phys. (1988) 115: 127. doi:10.1007/BF01238855


We construct an action-angle transformation for the Calogero-Moser systems with repulsive potentials, and for relativistic generalizations thereof. This map is shown to be closely related to the wave transformations for a large classl of Hamiltonians, and is shown to have remarkable duality properties. All dynamics inl lead to the same scattering transformation, which is obtained explicitly and exhibits a soliton structure. An auxiliary result concerns the spectral asymptotics of matrices of the formM exp(tD) ast→∞. It pertains to diagonal matricesD whose diagonal elements have pairwise different real parts and to matricesM for which certain principal minors are non-zero.

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© Springer-Verlag 1988