Symmetry group classification of three-dimensional Hamiltonian systems Original Research Article

We present some results on the symmetry group classification for an autonomous Hamiltonian system with three degrees of freedom. The potentials considered are natural, i.e., depend on the position variables only and the symmetries considered are Lie point symmetries. With the exception of the harmonic oscillator or a free particle where the dimension is 24, we obtain all dimensions between 1 and 12, except 8.