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

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.

6 pages

References in corpus (1)

• Dynamics in one complex variable: introductory lectures

Cited by in corpus (1)

• The Briot-Bouquet systems and the center families for holomorphic dynamical systems