Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 8 of 8 for “"Cantor Sets"”.
-
Continued Radicals and Cantor Sets
<p>We examine the formation of sets homeomorphic to the ternary Cantor set by continued radicals. We determine properties of bridges and gaps and calculate the thickness of the Cantor set. From this we apply information from continued fractions to continued radicals to obtain new results. We also …
-
The noncommutative geometry of ultrametric cantor sets
… of a manifold is created for an ultrametric Cantor set using the techniques of Noncommutative Geometry. In particular, a spectral triple is created that can recover much of the fractal geometry of the original Cantor set. It is shown that this spectral triple can recover the metric, the upper …
-
Geometry of Fractal Squares
This paper will examine analogues of Cantor sets, called fractal squares, and some of the geometric ways in which fractal squares raise issues not raised by Cantor sets. Also discussed will be a technique using directed graphs to prove bilipschitz equivalence of two fractal squares.
-
Quasiconformal Groups
… L(G) is positive. We also prove that the general Cantor sets are uniformly perfect. We consider quasiconformal mappings, quasisymmetric mappings, and weakly quasiconformal mappings in metric spaces. We show that in Loewner spaces the fourth definition of quasiconformal mappings, i.e., the ring …
-
Geometry of Self-Similar Sets
This paper examines self-similar sets and some of their properties, including the natural equivalence relation found in bilipschitz equivalence. Both dimension and preservation of paths are determined to be invariant under this equivalence. Also, sophisticated techniques, one involving the use of …
-
Hausdorff Dimension of Wildly Embedded Zero Dimensional Subspaces of R³
No abstract prepared.
-
On the Fourier decay and the dimension of self-similar measures
… known. In the final chapter, certain random subsets of Cantor sets are studied. The problem was introduced in \cite{allaart-jones} where both an upper and lower bound for the dimension of these sets was shown. Here, the precise value of the dimension is calculated.