Title: Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars),
Abstract: In this paper, we construct global action-angle variables for a certain
two-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars'
ideas on the translation invariant models, the proposed action-angle variables
come from a thorough analysis of the commutation relation obeyed by the Lax
matrix, whereas the proof of their canonicity is based on the study of the
scattering theory. As a consequence, we show that the van Diejen system of our
interest is self-dual with a factorized scattering map. Also, in an appendix by
S. Ruijsenaars, a novel proof of the spectral asymptotics of certain
exponential type matrix flows is presented. This result is of crucial
importance in our scattering-theoretical analysis.