A fast algorithmic way to calculate the degree growth of birational mappings

Abstract

We present an algorithmic method for the calculation of the degrees of the iterates of birational mappings, based on Halburd's method for obtaining the degrees from the singularity structure of the mapping. The method uses only integer arithmetic with additions and, in some cases, multiplications by small integers. It is therefore extremely fast. Several examples of integrable and non-integrable mappings are presented. In the latter case the dynamical degree we obtain from our method is always in agreement with that calculated by previously known methods.