Action-angle duality between the C -type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models

In a symplectic reduction framework we construct action-angle systems of canonical coordinates for both the hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen integrable models associated with the C root system. The presented dual reduction picture permits us to establish the action-angle duality between these many-particle systems.