The classical hyperbolic Askey–Wilson dynamics without bound states

We construct an explicit action–angle map for the classical hyperbolic Askey–Wilson dynamics (also known as the relativistic $BC_1$ Calogero–Moser system), restricting the four coupling constants such that no bound states occur. Its features are exact classical analogues of features previously obtained for the quantum eigenfunction transformation. Our construction involves neither scattering theory nor a Lax matrix; instead, it is based on a certain self-duality identity.