Dynamical Classification of a Family of Birational Maps of C2 via Algebraic Entropy

Abstract

This work dynamically classifies a 9-parametric family of birational maps f: C2→ C2. From the sequence of the degrees dn of the iterates of f, we find the dynamical degree δ(f) of f. We identify when dn grows periodically, linearly, quadratically or exponentially. The considered family includes the birational maps studied by Bedford and Kim (Mich Math J 54:647–670, 2006) as one of its subfamilies.