Raines, Brian Edward, 1975-Jones, Leslie Braziel.Baylor University. Dept. of Mathematics.2009-06-012009-06-012009-052009-06-01http://hdl.handle.net/2104/5311Includes bibliographical references (p. 66-68).We explore the endpoint structure of the inverse limit space of unimodal maps such that the restriction of the map to the ω-limit set of the critical point is topologically conjugate to an adding machine. These maps fall into the infinitely renormalizable unimodal family or the family of strange adding machines. A unimodal map, f, is renormalizable if there exists a restrictive interval J in its domain of period n such that J contains the critical point and fn : J → J is a unimodal map. If the renomalization process can be repeated infinitely often, we have an infinitely renormalizable map. Strange adding machines, however, are not renormalizable, and understanding the dynamical differences in these two families of maps is one of our goals. We give a characterization of the kneading sequence structure for these strange adding machines, and use this characterization to provide an example of a strange adding machine for which the set of folding points and the set of endpoints are not equal in the inverse limit space. We show that in the case of infinitely renormalizable maps, these two sets will always coincide. We extend our endpoint result by considering maps on finite graphs.iv, 68 p.95451 bytes325655 bytesapplication/pdfapplication/pdfen-USBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.Calculators.Mapping (Mathematics)Topological spaces.Topological dynamics.ThesisWorldwide access