Capture Zones of the Family of Functions λz[sup m]exp(z).

We consider the family of entire transcendental maps given by F[sub λ,m](z)=λz[sup m]exp(z) where m≥2. All functions F[sub λ,m] have a superattracting fixed point at z=0, and a critical point at z = -m. In the dynamical plane we study the topology of the basin of attraction of z=0. In the parameter plane we focus on the capture behavior, i.e. λ values such that the critical point belongs to the basin of attraction of z=0. In particular, we find a capture zone for which this basin has a unique connected component, whose boundary is then nonlocally connected. However, there are parameter values for which the boundary of the immediate basin of z=0 is a quasicircle. [ABSTRACT FROM AUTHOR]