Indecomposability in inverse limits.

Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and set-valued inverse limits of arbitrary compacta. Using the theory of Hubbard trees, the trunk of the Julia set of a postcriticallly finite polynomial is introduced. Using this trunk, a characterization of indecomposability is provided for inverse limits of post-critically finite polynomials restricted to their Julia sets. Inverse limits with upper semicontinuous set-valued bonding maps are also examined. We provide necessary and sufficient conditions for inverse limits of upper semicontinuous functions to have the full projection property, answering a question posed by Ingram. The full projection property is an important tool in the study of indecomposable inverse limits. A characterization of the full projection property for arbitrary compacta is given based solely on the dynamics of the bonding functions and a second characterization is given for the class of continuum-valued maps of trees that are residual-preserving.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2010

Author dc:creator

• Williams, Brian R. (Brian Robert), 1982-

Advisor dc:contributor.advisor

• Ryden, David James, 1971-

• Inverse limits.
• Julia sets.
• Indecomposability.
• Upper semicontinuous functions.

Statement dc:rights

• Baylor University works 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 libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/8067

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/8067