11-40 Heinz Hanßmann
Non-degeneracy conditions in KAM theory (780K, PostScript) Mar 5, 11
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Abstract. Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both the unperturbed and the perturbed torus. A non-degeneracy condition enforces a sufficiently large subset of the unperturbed tori to be non-resonant and thus yields persistence. In the past 60 years various such conditions have been formulated and a number of them are reviewed here.

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