Calculating the algebraic entropy of mappings with unconfined singularities
Résumé
We present a method for calculating the dynamical degree of a mapping with unconfined singularities.
It is based on a method introduced by Halburd for the computation of the growth of the iterates of a
rational mapping with confined singularities. In particular, we show through several examples how simple
calculations, based on the singularity patterns of the mapping, allow one to obtain the exact value of the
dynamical degree for non-integrable mappings that do not possess the singularity confinement property.
We also study linearizable mappings with unconfined singularities to show that in this case our method
indeed yields zero algebraic entropy