UNT Theses and Dissertations - 4 Matching Results

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Topological Conjugacy Relation on the Space of Toeplitz Subshifts

Description: We proved that the topological conjugacy relation on $T_1$, a subclass of Toeplitz subshifts, is hyperfinite, extending Kaya's result that the topological conjugate relation of Toeplitz subshifts with growing blocks is hyperfinite. A close concept about the topological conjugacy is the flip conjugacy, which has been broadly studied in terms of the topological full groups. Particularly, we provided an equivalent characterization on Toeplitz subshifts with single hole structure to be flip invari… more
Date: August 2022
Creator: Yu, Ping
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Continuity of Hausdorff Dimension of Julia Sets of Expansive Polynomials

Description: This dissertation is in the area of complex dynamics, more specifically focused on the iteration of rational functions. Given a well-chosen family of rational functions, parameterized by a complex parameter, we are especially interested in regularity properties of the Hausdorff dimension of Julia sets of these polynomials considered as a function of the parameters. In this dissertation I deal with a family of polynomials of degree at least 3 depending in a holomorphic way on a parameter, focusi… more
Date: August 2022
Creator: Wilson, Timothy Charles
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries

The D-Variant of Transfinite Hausdorff Dimension

Description: In this lecture we introduce a new transfinite dimension function for metric spaces which utilizes Henderson's topological D-dimension and ascribes to any metric space either an ordinal number or the symbol Ω. The construction of our function is motivated by that of Urbański's transfinite Hausdorff dimension, tHD. Henderson's dimension is a topological invariant, however, like Hausdorff dimension and tHD the function presented will be invariant under bi-Lipschitz continuous maps and generally n… more
Date: May 2022
Creator: Decker, Bryce
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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On the Descriptive Complexity and Ramsey Measure of Sets of Oracles Separating Common Complexity Classes

Description: As soon as Bennett and Gill first demonstrated that, relative to a randomly chosen oracle, P is not equal to NP with probability 1, the random oracle hypothesis began piquing the interest of mathematicians and computer scientists. This was quickly disproven in several ways, most famously in 1992 with the result that IP equals PSPACE, in spite of the classes being shown unequal with probability 1. Here, we propose what could be considered strengthening of the random oracle hypothesis, using a st… more
Date: August 2022
Creator: Creiner, Alex
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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