  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.
