DYNAMICS NEAR THE ESSENTIAL SINGULARITY OF A CLASS OF ENTIRE VECTOR-FIELDS

We investigate the dynamics near the essential singularity at infinity for a class of zero-free entire vector fields of finite order, i.e., those of the form f(z) = e(P)(z) where P(z) = z(d) or P(z) = a z2 + b z + c. We show that the flow generated by such a vector field has a ''bouquet of flowers'' attached to the point at infinity.