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
Cedarville University School or 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.
Recommended Citation
Averbeck, Nathan, "Chaos in Dendritic and Circular Julia Sets" (2016). Faculty Dissertations. 105.
https://digitalcommons.cedarville.edu/faculty_dissertations/105
