Indecomposability in inverse limits.

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dc.contributor.advisorRyden, David James, 1971-
dc.contributor.authorWilliams, Brian R. (Brian Robert), 1982-
dc.contributor.departmentMathematics.en
dc.contributor.otherBaylor University. Dept. of Mathematics.en
dc.date.accessioned2010-10-08T16:32:06Z
dc.date.available2010-10-08T16:32:06Z
dc.date.copyright2010-08
dc.date.issued2010-10-08T16:32:06Z
dc.descriptionIncludes bibliographical references (p. ).en
dc.description.abstractTopological 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.en
dc.description.degreePh.D.en
dc.description.statementofresponsibilityby Brian R. Williams.en
dc.format.extent71361 bytes
dc.format.extent443458 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/2104/8067
dc.language.isoen_USen
dc.rightsBaylor 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.en
dc.rights.accessrightsWorldwide access.en
dc.rights.accessrightsAccess changed 3/18/13.
dc.subjectInverse limits.en
dc.subjectJulia sets.en
dc.subjectIndecomposability.en
dc.subjectUpper semicontinuous functions.en
dc.titleIndecomposability in inverse limits.en
dc.typeThesisen

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