Chaos in dendritic and circular Julia sets.

dc.contributor.advisor	Raines, Brian Edward, 1975-
dc.creator	Averbeck, Nathan, 1985-
dc.date.accessioned	2016-09-01T14:14:32Z
dc.date.available	2016-09-01T14:14:32Z
dc.date.created	2016-08
dc.date.issued	2016-07-01
dc.date.submitted	August 2016
dc.date.updated	2016-09-01T14:14:32Z
dc.description.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.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/2104/9834
dc.language.iso	en
dc.rights.accessrights	Worldwide access.
dc.subject	Chaos. Dendrite. Julia set. Kneading sequence.
dc.title	Chaos in dendritic and circular Julia sets.
dc.type	Thesis
dc.type.material	text
thesis.degree.department	Baylor University. Dept. of Mathematics.
thesis.degree.grantor	Baylor University
thesis.degree.level	Doctoral
thesis.degree.name	Ph.D.