The Briot-Bouquet systems and the center families for holomorphic dynamical systems
Dynamical Systems
2013-07-16 v1 Classical Analysis and ODEs
Complex Variables
Abstract
We give a complete solution to the existence of isochronous center families for holomorphic dynamical systems. The study of center families for n-dimensional holomorphic dynamical systems naturally leads to the study of (n-1)-dimensional Briot-Bouquet systems in the phase space. We first give a detailed study of the Briot-Bouquet systems. Then we show the existence of isochronous center families in the neighborhood of the equilibrium point of three-dimensional systems based on the two-dimensional Briot-Bouquet theory. The same approach works in arbitrary dimensions.
Keywords
Cite
@article{arxiv.1307.3823,
title = {The Briot-Bouquet systems and the center families for holomorphic dynamical systems},
author = {Feng Rong},
journal= {arXiv preprint arXiv:1307.3823},
year = {2013}
}
Comments
13 pages, to appear in Adv. Math