On the degree of iterates of automorphisms of the affine plane
Let \(f\) be a polynomial automorphism of the affine space \(\mathbb C^2\). The author studies the iterations \(f^n=f\circ\cdots\circ f\) of \(f\). Let \(\tau:=\deg f^2\slash\deg f\). He proves that: 1. If \(\tau\leq 1\) then the sequence \((\deg f^n)_{n\in\mathbb N}\) is periodic for large \(n\), 2. If \(\tau>1\) then \(\tau\) is an integer and the sequence \((\deg f^n)_{n\in\mathbb N}\) is a geometric progression of the ratio \(\tau\).
scientific article; zbMATH DE number 1275772