On the Periodic Orbits of Piecewise Holomorphic Systems on ℂ2

In this paper, we propose an analytic framework to characterize centers in piecewise holomorphic systems on Formula: see text by analyzing the structure of periodic orbits in the associated real systems. For three representative classes of such systems, we establish necessary and sufficient conditions for the existence of a simple pseudo-center in each case, and we determine the dimension of the set of periodic orbits in the corresponding real systems when the simple pseudo-center conditions are not satisfied.