The space of initial conditions for linearizable mappings

We apply the algebraic–geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearization. The main difference with respect to the previous studies is that the linearizable mappings have generically unconfined singularities. Despite this fact we are able to provide a complete description of the dynamics of these mappings and derive rigorously their growth properties.