= Solution
\b[More than three integrals occur when additional symmetry or degeneracy restricts motion beyond a generic three-frequency invariant torus.] In a time-independent central <gravitational potential>, energy and the three components of <specific angular momentum> are four generically independent <isolating integrals>. They fix the orbital plane as well as the radial-motion parameters. A nonclosed planar rosette typically has two-dimensional orbit closure, rather than a three-dimensional <invariant torus>.
The <Kepler orbit> is a stronger example. In addition to $E$ and $\mathbf L$, the conserved <Laplace-Runge-Lenz vector>
$$
\mathbf A=\mathbf v\times\mathbf L-\mu\frac{\mathbf r}{r},\qquad \mu=GM,
$$
fixes the apsidal direction. Its constraints $\mathbf A\cdot\mathbf L=0$ and $A^2=\mu^2+2EL^2$ leave five independent integrals among $E,\mathbf L,\mathbf A$. It is a maximally <superintegrable Hamiltonian system>, with closed nondegenerate bound orbits.
More than three integrals need not form a set of <Poisson-commuting functions>; the three-integral limit applies to an independent commuting set, rather than to every conserved orbit constraint. At a nonstationary point in six-dimensional <phase space>, integral gradients annihilate the nonzero flow vector, so at most five are independent. This explains the <isolating integrals and orbital closure dimension> count. A resonance on one isolated orbit does not by itself prove an additional smooth global integral on a neighborhood.
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