Dynamical Classification of a Family of Birational Maps of C-2 via Algebraic Entropy

摘要

This work dynamically classifies a 9-parametric family of birational maps f : C-2 -> C-2. From the sequence of the degrees d(n) of the iterates of f, we find the dynamical degree delta(f) of f. We identify when d(n) 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.