= Solution
The <Arnold-Liouville theorem> states that if $F_1,\ldots,F_n$ are independent commuting first integrals and a connected component $L$ of a regular common level
$$
F_1=c_1,\ldots,F_n=c_n
$$
is compact, then $L$ is diffeomorphic to the $n$-torus. A neighbourhood of $L$ admits <action-angle variables> $(I_1,\ldots,I_n,\theta_1,\ldots,\theta_n)$ in which
$$
\omega=\sum_jdI_j\wedge d\theta_j,
\qquad H=H(I),
$$
and the motion is linear on each invariant torus:
$$
\dot I_j=0,
\qquad
\dot\theta_j=\frac{\partial H}{\partial I_j}.
$$
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