The purpose of this paper is a pedagogical one. We provide a short and self-contained account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic map of the complex plane can be locally linearized near a fixed point under certain conditions on the multiplier. The main proof is adapted from Bruno’s work.

中文翻译：

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西格尔-布鲁诺线性化定理

本文的目的是教学目的。我们提供了由布鲁诺改进的西格尔定理的简短且独立的说明，该定理指出，在乘数上的某些条件下，复平面的全纯映射可以在固定点附近局部线性化。主要证明改编自布鲁诺的作品。