Autonomous three-dimensional Newtonian systems which admit Lie and Noether point symmetries

摘要

We determine the autonomous three-dimensional Newtonian systems which admit Lie point symmetries and the three-dimensional autonomous Newtonian Hamiltonian systems which admit Noether point symmetries. We apply the results in order to determine the two-dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether point symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.