Indecomposability in inverse limits.

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dc.contributor.advisor Ryden, David James, 1971- Williams, Brian R. (Brian Robert), 1982-
dc.contributor.other Baylor University. Dept. of Mathematics. en 2010-08
dc.description.abstract 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. en
dc.rights Baylor 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 for inquiries about permission. en
dc.subject Inverse limits. en
dc.subject Julia sets. en
dc.subject Indecomposability. en
dc.subject Upper semicontinuous functions. en
dc.title Indecomposability in inverse limits. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Worldwide access. en
dc.rights.accessrights Access changed 3/18/13.
dc.contributor.department Mathematics. en

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