CAPTURE ZONES OF THE FAMILY OF FUNCTIONS $\lambda z^m \exp(z)$ Nuria Fagella*, Antonio Garijo** *Departament de Matematica aplicada i Analisi Universitat de Barcelona Gran Via 585 08005 Barcelona Spain e-mail: fagella@maia.ub.es *Departament d'Enginyeria informatica i Matematiques Universitat Rovira i Virgili Av. Paisos Catalans 26 13007 Tarragona, Spain agarijo@etse.urv.es ABSTRACT We consider the family of entire transcendental maps given by $F_{\lambda,m} (z ) \, = \, \lambda z^m \exp(z) $ where $ m \ge 2$. All functions $F_{\lambda,m}$ 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 in the capture behaviour, i.e., $\lambda$ 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 non-locally connected. However, there are parameter values for which the boundary of the immediate basin of $z=0$ is a quasicircle.