Integrable Hamiltonian systems with two degrees of freedom associated with holomorphic functions (Q1586712)

This paper deals with integrable systems with two degrees of freedom that are integrable in the Liouville sense and are obtained as real and imaginary parts of a polynomial (or entire) complex function in two complex variables. The authors propose definitions for the actions of the Riemann-Liouville systems and present a computation method based on a complex Hamilton-Jacobi equation. Moreover, they apply these techniques to several examples including those recently considered in relation to perturbations of the Ruijsenaars-Schneider system.