  In this note we present and briefly discuss results, which include as a
particular case the theorem announced in [L. Biasco, and L. Chierchia. On the
measure of Lagrangian invariant tori in nearly-integrable mechanical systems.
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), 1-10], concerning
the typical behaviour of nearly-integrable mechanical systems with generic
analytic potentials.
