A contraction-mapping proof of Koenigs’ theorem

Mestel, Benjamin D. (2014). A contraction-mapping proof of Koenigs’ theorem. Aequationes Mathematicae, 88(1-2) pp. 35–38.

DOI: https://doi.org/10.1007/s00010-014-0265-7

Abstract

We give a simple, functional analytic proof of Koenigs’ theorem on the linearisation of a complex analytic function in a neighbourhood of a hyperbolic fixed point. The proof uses the contraction mapping principle in the nonlinearity norm.

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