On the conservation of adiabatic invariants for a system of coupled rotators

We study the accuracy of the conservation of adiabatic invariants in a model of n weakly coupled rotators. Most attention is devoted to n = 2 and frequency ω = (ω1, ω2), with ω2/ω1 quadratic irrational. We apply a heuristic approximation scheme, going back to Jeans and to Landau and Teller, and perform a very accurate numerical check of the result, observing a quite remarkable agreement.