article

Title: Growth of attraction rates for iterates of a superattracting germ in dimension two

Authors: Matteo Ruggiero and William Gignac

Issue: Volume 63 (2014), Issue 4, 1195-1234

Abstract:

$We study the sequence of attraction rates of iterates of a dominant superattracting holomorphic fixed point germ $f\colon(\mathbb{C}^2,0)\to(\mathbb{C}^2,0)$. By using valuative techniques similar to those developed by Favre-Jonsson, we show that this sequence eventually satisfies an integral linear recursion relation, which, up to replacing $f$ by an iterate, can be taken to have order at most two. In addition, when the germ $f$ is finite, we show the existence of a bimeromorphic model of $(\mathbb{C}^2,0)$ where $f$ satisfies a weak local algebraic stability condition.$