CENTER FAMILIES IN 2-DIMENSIONAL COMPLEX HOLOMORPHIC DYNAMICAL-SYSTEMS

We consider a two-dimensional complex holomorphic dynamical system. In particular, we use the singular point theory of C. H. Briot and J. C. Bouquet to establish the existence of complex holomorphic invariant m anifolds of the system in the neighbourhood of an equilibrium point wi th two purely imaginary eigenvalues. Consequently, this enables us to establish the existence of isochronous centre families in the neighbou rhood of the equilibrium point. The results are exhibited by applicati on to the complex Takens-Bogdanov system.