Teichmüller theory and critically finite endomorphisms

We present a systematic way to generate critically finite endomorphisms of Pⁿ${\mathbb{P}}^n$. These maps arise in the context of Teichmüller theory, specifically in Thurston?s topological characterization of rational maps. The dynamical objects for the endomorphisms correspond to central objects from Thurston?s theorem. Our theorems build infinitely many of these endomorphisms; in fact, a large number of examples of critically finite endomorphisms of Pⁿ${\mathbb{P}}^n$ found in the literature arise from this construction.