A proof of this theorem relies on finding systems with frequencies that are strongly non-resonant, which means that they satisfy the "small divisor" condition.
One version of this theorem was developed using twist maps in a paper concerning invariant curves of area-preserving maps on an annulus, and one condition of its applicability is that the map winding number be sufficiently irrational. A proof of this theorem relies on finding systems with frequencies that are strongly non-resonant, which means that they satisfy the "small divisor" condition. Although this theorem does not provide a way to tell whether a given orbit falls on an invariant torus, it does preclude the onset of ergodicity if its conditions are met. As a consequence of this theorem, the non-resonant toruses on which quasiperiodic motion occurs remain undestroyed. For ten points, identify this theorem which states that for sufficiently small perturbations of an integrable Hamiltonian system the majority of the trajectories remain stable, named for the Russian physicist who first proposed it and two others.
One version of this theorem was developed using twist maps in a paper concerning invariant curves of area-preserving maps on an annulus, and one condition of its applicability is that the map winding number be sufficiently irrational.
Kolmogorov-Arnold-Moser theorem [accept any permutation of initials]