Journal of Statistical Physics, Vol. 56, Nos. 1/2, 1989. p. 83-98.
Let f be a two-dimensional area-preserving twist map. Given an irrational rotation number co in the rotation interval off, there is an invariant recurrent set on which f preserves the circular ordering and which has rotation number co. For large nonlinearity, the parameter regime we are interested in, this set is a
Cantor set. We show that well-ordered (minimizing) sets with rotation numbers close to co are exponentially close to the Cantor set under study. The detailed configuration of well-ordered (minimizing) sets is universal and depends on one parameter, namely the Lyapunov coefficient of the Cantor set. There is a quantitative correspondence between this and similar behavior in the noninvertible circle map.