The Briot-Bouquet systems and the center families for holomorphic dynamical systems
arXiv:1307.3823 · doi:10.1016/j.aim.2013.06.021
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.
13 pages, to appear in Adv. Math