Distortion elements in the group of diffeomorphisms of the 2-sphere

We characterize dynamics of every distortion element in the group of diffeomorphisms of the 2-sphere that has at least two fixed points and another recurrent point. The key result is that if f is such a diffeomorphism, then the homeomorphism fₐₙₙ , which is a lift of the homeomorphism of the closed annulus Ā obtained from S² by blowing up two fixed points of f to the universal covering space of Ā , has a unique rotation number. Moreover, we find the differential of such a distortion element in the group of diffeomorphisms of the 2-sphere at each fixed point up to conjugacy.