Abstract:

We consider the family of entire transcendental maps given by $f$_a(z)=ae^a(z-(1-a))exp(z) where $a$ is a complex parameter. All functions $f$_a have a superattracting fixed point at $z=-a$ and an asymptotical value at $z=0$. S. Morosawa proved that the Julia set of $f$_a is a Sierpinski curve for $a>1$. We show the existence of a dynamically defined indecomposable continuumembbeded in the Julia set for all escaping parameters $a>3$. We also study the relation between this indecomposable continuum and the immediate basin of attraction of $z=-a$.