= Superintegrable Hamiltonian system
A <superintegrable Hamiltonian system> with $n$ degrees of freedom has more than $n$ functionally independent <integrals of motion>, including an integrable set of $n$ in involution. At a regular nonzero <Hamiltonian vector field>, at most $2n-1$ independent integral differentials can annihilate the flow. A maximally superintegrable system attains that bound. The three-dimensional <Kepler orbit> has five independent integrals through energy, angular momentum and the <Laplace-Runge-Lenz vector>. A closed orbit on one isolated resonance is weaker than maximal superintegrability on an open phase-space region.
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