Smooth approximation of mather sets of monotone twist mappings

In the theory of monotone twist mappings of a cylinder one constructs for every rotation number α invariant minimal sets M_α. In this paper an approximation of these Mather sets by smooth invariant curves M^v_α is devised, which for v → 0 converge to M_α almost everywhere. The main point of the construction is that the approximating curves M^v_α form for v > 0 a smooth foliation. The approximation is achieved with the help of a regularized version of the Percival variational problem. © 1994 John Wiley & Sons, Inc.