IUMJ

Title: B\"ottcher Coordinates

Authors: Xavier Buff, Adam Epstein and Sarah Koch

Issue: Volume 61 (2012), Issue 5, 1765-1799

Abstract:

A well-known theorem of B\"ottcher asserts that an analytic germ $f:(\mathbb{C},0)\to(\mathbb{C},0)$ which has a superattracting fixed point at $0$, more precisely of the form $f(z)=az^k+o(z^k)$ for some $a\in\mathbb{C}^{*}$, is analytically conjugate to $z\mapsto az^k$ by an analytic germ $\phi:(\mathbb{C},0)\to(\mathbb{C},0)$ which is tangent to the identity at $0$. In this article, we generalize this result to analytic maps of several complex variables.