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| dc.contributor.author | Sattler, Elizabeth | |
| dc.description.abstract | In this thesis, a subfractal is the subset of points in the attractor of an iterated functionsystem in which every point in the subfractal is associated with an allowable word from a subshifton the underlying symbolic space. In the case in which (1) the subshift is a subshift of nitetype with an irreducible adjacency matrix, (2) the iterated function system satis es the open setcondition, and (3) contractive bounds exist for each map in the iterated function system, we ndbounds for both the Hausdor and box dimensions of the subfractal, where the bounds depend bothon the adjacency matrix and the contractive bounds on the maps. We extend this result to so csubshifts, a more general subshift than a subshift of nite type, and to allow the adjacency matrixto be reducible. The structure of a subfractal naturally de nes a measure on Rn. For an iteratedfunction system which satis es the open set condition and in which the maps are similitudes, we construct an invariant measure supported on a subfractal induced by a subshift of nite type. Forthis speci c measure, we calculate the local dimension for almost every point, and hence calculate the Hausdor dimension for the measure. | en_US |
| dc.publisher | North Dakota State University | en_US |
| dc.rights | NDSU Policy 190.6.2 | |
| dc.title | Subfractals Induced by Subshifts | en_US |
| dc.type | text/dissertation | en_US |
| dc.type | movingimage/video | en_US |
| dc.date.accessioned | 2016-06-06T13:52:08Z | |
| dc.date.available | 2016-06-06T13:52:08Z | |
| dc.date.issued | 2016 | |
| dc.identifier.uri | http://hdl.handle.net/10365/25660 | |
| dc.description.sponsorship | ND-EPSCoR | |
| dc.rights.uri | https://www.ndsu.edu/fileadmin/policy/190.pdf | |
| ndsu.degree | Doctor of Philosophy (PhD) | |
| ndsu.college | College of Science and Mathematics | |
| ndsu.department | Mathematics | |
| ndsu.program | Mathematics | |
| ndsu.advisor | Çömez, Doğan |
Subshifter
Subshifts with property are constructed from a class of directed graphs. As special cases the Markov–Dyck shifts are shown to have property. The semigroups that are associated to -graph shifts with Property are determined. A subshift of nite type. We brie y de ne both topological and measure-theoretic dynamical systems in more generality. The three types of entropy de ned here. SUBSHIFT adopts his new alias on the release of a forward-facing tech house two-tracker by the name of ‘My Mind / Let Me’ via IN / ROTATION. On his newly updated bio, the fast-emerging house producer succinctly captures the ethos of his project with a prime choice of words: “A constant state.