  We characterize the infinitesimal generator of a semigroup of linear
fractional self-maps of the unit ball in $\mathbb C^n$, $n\geq 1$. 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.
