From an iteration formula to Poincar\'{e}'s Isochronous Center Theorem for holomorphic vector fields
Dynamical Systems
2007-05-23 v2 Complex Variables
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. Poincar\'{e}, for the condition under which a singularity of a holomorphic vector field is an isochronous center.
Cite
@article{arxiv.math/0511622,
title = {From an iteration formula to Poincar\'{e}'s Isochronous Center Theorem for holomorphic vector fields},
author = {Guang Yuan Zhang},
journal= {arXiv preprint arXiv:math/0511622},
year = {2007}
}
Comments
6 pages