This is related to classical Hamiltonian mechanics. There is something wrong in the following argument but I cannot pinpoint where exactly the pitfall is: Consider an arbitrary (smooth) Hamiltonian (let us assume conservative) and 2n phase space coordinates (q,p). The Hamiltonian flow gives the evolution starting the initial conditions (q(q0,p0,t),p(q0,p0,t)). Now, clearly the inverse function (q0(q,p,t),p0(q,p,t)) provides 2n constants of motion: for any point (q,p) in the orbit and t one can reconstruct the initial values of the coordinates, obtaining always the same values. In addition the transformation from (q,p) to (q0,p0) is a canonical one, so the Poisson brackets between the various q0 vanish. I would say that obviously the various q0(q,p,t) are functionally independent. So apparently, any Hamiltonian system is integrable in the sense of Liouville (the fact that these n functions q0(q,p,t) are very complicated is a different matter). Can any one point out to me where is the fallacy? Thanks.