Existence of indecomposable continua for unstable exponentials
by
Monica Moreno-Rocha
Boston University

In the parameter plane for the complex exponential family E_v(z)=v e^z there exist parameters for which the orbit of zero lies on dynamical curves which are invariant under a fixed power of E_v. At the same time, the orbit of zero tends to infinity and in these cases, the Julia set for E_v is the whole complex plane. We construct fundamental regions based on these dynamical curves. Inside each region, we show the existence of an invariant set that, once properly compactified, turns to be an indecomposable continuum. This is a generalization of the construction given by R.L. Devaney when v > 1/e.

Date received: January 25, 2001