Chaos in Dendritic and Circular Julia Sets
Date of Award
Doctor of Philosophy (Ph.D.)
Institution Granting Degree
Cedarville University School or Department
Science and Mathematics
Brian Raines, D.Phil.
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.
Averbeck, Nathan, "Chaos in Dendritic and Circular Julia Sets" (2016). Faculty Dissertations. 105.