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dc.contributor.advisorRaines, Brian Edward, 1975-
dc.contributor.authorSherman, Casey L.
dc.date.accessioned2012-11-29T16:22:23Z
dc.date.available2012-11-29T16:22:23Z
dc.date.copyright2012-08
dc.date.issued2012-11-29
dc.identifier.citationGood, C., Greenwood, S., Raines, B. E., & Sherman, C. L. "A compact metric space that is universal for orbit spectra of homeomorphisms." Advances in Mathematics 229, #5 (2012): 2670-2685.en_US
dc.identifier.citationSherman, Casey. "A Lebesgue-like measure for inverse limit spaces of piecewise strictly monotone maps of an interval." Topology and its Applications 159, 8 (2012): 2062-2070.en_US
dc.identifier.urihttp://hdl.handle.net/2104/8516
dc.description.abstractIn this dissertation we answer the following question: If X is a Cantor set and T: X → to X is a homeomorphism, what possible orbit structures can T have? The answer is given in terms of the orbit spectrum of T. If X is a Cantor set, then there is a homeomorphism T : X → to X with σ(T) = (0, ζ, σ₁, σ₂, σ₃, …) if and only if one of the following holds: 1) ζ = 0, there exists k ∈ N and a set {n₁ … ,nk} with σ _{n_i} > 0 for each 1 ≤ i ≤ k such that if σ _j > 0 then there exists i ∈ {1, 2, …, k} with n_i|j and there is an m ∈ N with σ _{mj} = c. 2) 1 ≤ ζ < c, {n: σ_ n= c} is infinite, and ∑ σ_ n : σ_ {mn} < c { for all m∈N} ≤ ζ, or 3) ζ = c.en_US
dc.language.isoen_USen_US
dc.publisheren
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_US
dc.subjectCantor set.en_US
dc.subjectHomeomorphism.en_US
dc.subjectOrbit structure.en_US
dc.subjectInverse limit space.en_US
dc.subjectDynamical systems.en_US
dc.subjectUniversal compact metric space.en_US
dc.titleOrbit structures of homeomorphisms.en_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.contributor.departmentMathematics.en_US
dc.contributor.schoolsBaylor University. Dept. of Mathematics.en_US


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