The Toda lattice is super-integrable
  We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action--angle coordinates introduced by Moser to solve the equations of motion. 
M. Agrotis, P. A. Damianou, C. Sophocleous