ABSTRACT
This chapter deals with the case that the Julia set is a Cantor set. The idea to characterize orbits by a sequence of symbols or integers has a long history. It occurs already in the study of Hadamard in 1898. A beautiful application is to the restricted three-body problem. The chapter describes an “explosion” in the Julia set. An explosion occurs at a parameter value for a family of functions whenever the Julia sets of the functions in the family change suddenly, when the parameter is reached, from a nowhere dense subset to all the plane. The chapter discusses the expansion and distortion properties of certain entire functions, and examines the connectivity of Julia sets.
