From an iteration formula to Poincaré’s Isochronous Center Theorem for holomorphic vector fields

Zhang, Guang

doi:10.1090/S0002-9939-07-08802-8

From an iteration formula to Poincaré’s Isochronous Center Theorem for holomorphic vector fields
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by Guang Yuan Zhang PDF

Proc. Amer. Math. Soc. 135 (2007), 2887-2891 Request permission

Abstract:

We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H. Poincaré, for the condition under which a singularity of a holomorphic vector field is an isochronous center.

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