Indecomposable continua in exponential dynamics

Abstract

In this paper we prove the existence of uncountably many indecomposable continua in the dynamics of complex exponentials of the form Eλ(z) = λez with λ 1/e. These continua contain points that share the same itinerary under iteration of Eλ. These itineraries are bounded but consist of blocks of 0's whose lengths increase, and hence these continua are never periodic. © 2002 American Mathematical Society.