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

Abstract

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.

Accepted for publication in Journal of Physics A: Math. and Theor.,13 pages

References in corpus (3)

• Lie and Noether symmetries of geodesic equations and collineations
• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere $S^2$ and the hyperbolic plane $H^2$
• Two dimensional dynamical systems which admit Lie and Noether symmetries

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