Arnold’s “Fundamental Theorem” on properly–degenerate systems [3, Chapter IV] is revisited and improved with particular attention to the relation between the perturbative parameters and to the measure of the Kolmogorov set. Relations with the planetary many–body problem are shortly discussed.
Chierchia, L., Pinzari, G. (2010). Properly-degenerate KAM theory (following V.I. Arnold). DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 3 (4), 545-578 [10.3934/dcdss.2010.3.545].