Kolmogorov flows theorem

Although in a weakly time-dependent flow all resonant tori disappear together with some of the nearly resonant tori around them, the Kolmogorov-Arnold-Moser theorem ensures that infinitely many invariant surfaces survive a small perturbation. For sufficiently small e the remaining invariant surfaces formed by quasiperiodic orbits, so called KAM tori, still occupy a non-zero volume of the phase space. The condition for a torus to survive a given perturbation is that its rotation number should be sufficiently far from any rational number so that the inequality... 

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