B\"ottcher coordinates
Dynamical Systems
2011-04-18 v1 Complex Variables
Abstract
A well-known theorem of B\"ottcher asserts that an analytic germ f:(C,0)->(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 C^*, is analytically conjugate to z->az^k by an analytic germ phi:(C,0)->(C,0) which is tangent to the identity at 0. In this article, we generalize this result to analytic maps of several complex variables.
Cite
@article{arxiv.1104.2981,
title = {B\"ottcher coordinates},
author = {Xavier Buff and Adam Epstein and Sarah Koch},
journal= {arXiv preprint arXiv:1104.2981},
year = {2011}
}