A completely integrable Hamiltonian system
Résumé
The dynamical system characterized by the Hamiltonian H( q , p )=∑ j,k=1 n p jp kf (q dj−q k ) with f(x)=λ+μ cos(νx)+μ′ sin(ν‖x‖) is completely integrable. Here n is an arbitrary positive integer and λ,μ,μ′,ν are 4 arbitrary constants (λ and μ real, μ′ and ν both real or both imaginary).