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, "primary" tori in a nearly--integrable, real--analytic Hamiltonian system is $O(\sqrt{\varepsilon})$, if $\varepsilon$ is the size of the perturbation. In this paper we discuss how the constant in front of $\sqrt{\varepsilon}$ depends on the unperturbed system and in particular on the phase--space domain. 
Luca Biasco and Luigi Chierchia
math.DS