On the Konigs function of semigroups of holomorphic self-maps of the unit disc

Let $(phi_t)$ be a semigroup of holomorphic self-maps of~$mathbb D$. In this note, we use an abstract approach to define the Konigs function of $(phi_t)$ and holomorphic models and show how to deduce the existence and properties of the infinitesimal generator of $(phi_t)$ from this construction.