Orbit structures of homeomorphisms.

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dc.contributor.advisor Raines, Brian Edward, 1975- Sherman, Casey L. 2012-08
dc.identifier.citation Good, 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.citation Sherman, 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.description.abstract In 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.publisher 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_US
dc.subject Cantor set. en_US
dc.subject Homeomorphism. en_US
dc.subject Orbit structure. en_US
dc.subject Inverse limit space. en_US
dc.subject Dynamical systems. en_US
dc.subject Universal compact metric space. en_US
dc.title Orbit structures of homeomorphisms. en_US
dc.type Thesis en_US Ph.D. en_US
dc.rights.accessrights Worldwide access en_US
dc.contributor.department Mathematics. en_US
dc.contributor.schools Baylor University. Dept. of Mathematics. en_US

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