Abstract

We consider in this talk the topology of certain invariant subsets of the Julia sets for the complex exponential family, $\lambda \; ez$, in the case where the Julia set is the whole complex plane. When $\lambda \; >\; 1/e$, it is known the existence of invariant subsets that can be countably compactified into indecomposable continua. In this talk we will provide an introduction to continuum theory and generalize the existence of invariant indecomposable continua for certain complex values of the parameter.