Explicit estimates on the measure of primary KAM tori

From KAM theory it follows that the measure of phase points which do not lie on Diophantine, Lagrangian, âprimaryâ tori in a nearly integrable, real-analytic Hamiltonian system is (Formula presented.), if (Formula presented.) is the size of the perturbation. In this paper we discuss how the constant in front of (Formula presented.) depends on the unperturbed system and in particular on the phase-space domain