Journal of Statistical Physics, Vol. 65, Nos. 3/4, 1991. p. 617-643.
One-parameter families of area-preserving twist maps of the form F_e(x, y)= (x + y + ef(x), y + ef(x)) are considered. Various invariant curves, for the maps corresponding to f(x) = sin x and f(x) = sin x + (1/50) sin(5x), are rigorously constructed for large values of the nonlinearity parameter e. For larger values of e, close to critical, some numerical experiments are briefly discussed.