HERMAN'S LAST GEOMETRIC THEOREM

We present a proof of Herman's Last Geometric Theorem asserting that if F is a smooth diffeomorphism of the annulus having the intersection property, then any given F-invariant smooth curve on which the rotation number of F is Diophantine is accumulated by a positive measure set of smooth invariant curves on which F is smoothly conjugated to rotation maps. This implies in particular that a Diophantine elliptic fixed point of an area preserving diffeomorphism of the plane is stable. The remarkable feature of this theorem is that it does not require any twist assumption.