“…Taking ε < ε 0 (H, δ/2, ρ/2), insures that if I 0 ∈ S g (H, δ, ρ) then it is at least ∆ away from the boundary of S g (H, δ/2, ρ/2), where ∆ = min(ρ/4, K 1 δ, K 2 δ| ln(2δ)|) and K 1,2 (H) are some constants depending on the unperturbed rotation rates (see Eq. 7,11). It follows that the map (14) The destroyed, resonant tori correspond to rational values of the modified rotation number…”