Abstract

Limits of a recently introduced n-particle difference Calogero-Moser system with elliptic potentials are studied. We obtain hyperbolic and rational difference Calogero-Moser systems with an eight-parameter external field and (finite) difference Toda chains with four-parameter potentials acting on the boundary particles. Hamiltonians for a number of known integrable n-particle systems, such as Ruijsenaars' relativistic Calogero-Moser and Toda models and their generalizations associated with classical root systems, can be seen as special cases of the Hamiltonians considered in this paper.