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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105081We 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 pagesDynamical SystemsComplex Variables32H50, 32M25, 37C27From an iteration formula to Poincaré's Isochronous Center Theorem for holomorphic vector fieldstext