= Integrals of an irrational two-frequency oscillator
{title2=$F=\phi(R_1,R_2)$}
On the regular set of two uncoupled oscillators with irrational frequency ratio, every continuous globally defined <integral of motion> is constant on each fixed-action <flat torus>, because every orbit is dense there. A differentiable integral is consequently a function of the two actions, so its <differential of a smooth map> lies in their span. Local angle combinations can still give extra local integrals; they fail to be single-valued on the torus.
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