Chaos in Dendritic and Circular Julia SetsFaculty Dissertations
Date of Award8-1-2016
Degree NameDoctor of Philosophy (Ph.D.)
Institution Granting DegreeBaylor University
Cedarville University School or DepartmentScience and Mathematics
First AdvisorBrian Raines, D.Phil.
AbstractWe 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.
Citation InformationNathan Averbeck. "Chaos in Dendritic and Circular Julia Sets" (2016)
Available at: http://works.bepress.com/nathan-averbeck/6/