Heinz Hanßmann
Non-degeneracy conditions in KAM theory
(780K, PostScript)

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.