Infinitesimal generators associated with semigroups of linear fractional maps

We characterize the infnitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C^n, n>=1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional maps if and only if it contains a linear fractional map for some positive time.