Title

Chaos in Dendritic and Circular Julia Sets

Date of Award

8-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Institution Granting Degree

Baylor University

Department

Science and Mathematics

First Advisor

Brian Raines, D.Phil.

Abstract

We demonstrate the existence of various forms of chaos (including transitive distributional chaos, w-chaos, topological chaos, and exact Devaney chaos) on two families of abstract Julia sets: the dendritic Julia sets DT and the "circular" Julia sets ԐT, whose symbolic encoding was introduced by Stewart Baldwin. In particular, suppose one of the two following conditions hold: either fc has a Julia set which is a dendrite, or (provided that the kneading sequence of c is Г-acceptable) that fc has an attracting or parabolic periodic point. Then, by way of a conjugacy which allows us to represent these Julia sets symbolically, we prove that fc exhibits various forms of chaos.