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

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

2005-11-25

arxiv.org/abs/math/0511622v2

Mathematics

Dynamical Systems

6 pages

Scientific paper

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. Poincar\'{e}, for the condition under which a singularity of
a holomorphic vector field is an isochronous center.

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