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| Title: | Inverse limits of permutation maps | |
| Author (s): | Beane, Robbie Allen, 1979- | |
| Advisor(s): | Charatonik, Wlodzimierz J. | |
| Issue Date: | 2008 | |
| Publisher: | Missouri University of Science and Technology | |
| Citation: | Beane, Robbie. "Inverse Limits of Permutation Maps." Ph.D. Dissertation, Mathematics, Missouri University of Science and Technology, 2008. | |
| Abstract: | "In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to study inverse limits on [0,1] with a single bonding map chosen from the one parameter family of logistic mappings. It is known that there is an open and dense subset of the parameter space for which the associated logistic maps have attracting periodic orbits. We show that any continuum generated by such a logistic map is homeomorphic to the inverse limit on [0,1] with some permutation bonding map. We close by providing a sufficient condition for the inverse limit on an interval with a single bonding map to fail to be a Kelley continuum, and applying this information to the logistic family"--Abstract, p. iii. | |
| Type: | Thesis/Dissertation text | |
| Copyright Notice: | These materials are protected under copyright by the original author. | |
| Link to this page: | ||
| URL: | ||
| Full Text: |
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| title | Inverse limits of permutation maps | |
| contributor.advisor | Charatonik, Wlodzimierz J. | |
| contributor.author | Beane, Robbie Allen, 1979- | |
| subject.LCSH | Continuum (Mathematics) | |
| subject.LCSH | Mappings (Mathematics) | |
| subject.LCSH | Permutations. | |
| subject.LCSH | Topology. | |
| date.issued | 2008 | |
| publisher | Missouri University of Science and Technology | |
| identifier.URI | ||
| identifier.citation | Beane, Robbie. "Inverse Limits of Permutation Maps." Ph.D. Dissertation, Mathematics, Missouri University of Science and Technology, 2008. | |
| identifier.oclc | 227351747 | |
| description | Includes bibliographical references (p. 71-73). | |
| description | Mode of access: World Wide Web. | |
| description | System requirements: Adobe Acrobat Reader; Internet browser. | |
| description | The entire thesis text is included in file. | |
| description | Thesis (Ph. D.)--Missouri University of Science and Technology, 2008. | |
| description | Title from title screen of thesis/dissertation PDF file (viewed May 9, 2008) | |
| description | Vita. | |
| description.abstract | "In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to study inverse limits on [0,1] with a single bonding map chosen from the one parameter family of logistic mappings. It is known that there is an open and dense subset of the parameter space for which the associated logistic maps have attracting periodic orbits. We show that any continuum generated by such a logistic map is homeomorphic to the inverse limit on [0,1] with some permutation bonding map. We close by providing a sufficient condition for the inverse limit on an interval with a single bonding map to fail to be a Kelley continuum, and applying this information to the logistic family"--Abstract, p. iii. | |
| description. statementOfResponsibility | by Robbie Allen Beane. | |
| type | Thesis/Dissertation | |
| type.DCMIType | text | |
| rights | These materials are protected under copyright by the original author. | |
| language.ISO639-2 | eng | |
| format.extent | vii, 74 p. : ill., digital, PDF file. | |
| date.accessioned | 2008-05-07T22:34:41Z | |
| date.available | 2008-05-14T13:28:55Z | |
| identifier.persist.URI | ||
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