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arXiv · 1104.2981

B\"ottcher coordinates

Xavier Buff·Adam Epstein·Sarah Koch
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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.

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Xavier Buff, Adam Epstein, Sarah Koch. 2011-04-15. B\"ottcher coordinates. https://arxiv.org/abs/1104.2981

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