English

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.

Keywords

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

R2 v1 2026-07-22T17:27:53.310Z