A class of linear fractional maps of the ball and their composition operators

We study a class of linear fractional self-maps of the ball which seems to be a good generalization of parabolic non-automorphisms of the unit disk. We give a normal form of these maps and use it to compute the spectrum of the composition operators induced by them. We also show that these composition operators are never hypercyclic. Applications are given to the study of more general linear fractional transformations.