Abstract:

We consider in this talk the question of accessibility of points in the Julia sets of complex exponential functions in the case where the exponential admits an attracting cycle. In the case of an attracting fixed point it is known that the Julia set is a Cantor bouquet and that the only points accessible from the basin are the endpoints of the bouquet. If the cycle has period two or greater, there are many more restrictions on which points in the Julia set are accessible. We give precise conditions for a point to be accessible in the periodic point case in terms of the kneading sequence for the cycle.