SubShift
| 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 |
A rank‐one subshift with bounded spacer parameter is a minimal dynamical system. A rank‐one subshift with unbounded spacer parameter has exactly one fixed point 1 Z. 2.3 Some basic facts. We identify some specific elements in a rank‐one subshift. A subshift or shift space is a closed subset of some full shift AZ that is invariant under the action of σ. For example, the set of binary sequences that do not contain the string 11 is a subshift of the 2-shift. It is closed because its complement is open: if a sequence contains 11 then every sequence sufficiently close to it does as well.
- Subshift meaning (mathematics) A set of infinite words representing the evolution of a discrete system, used in symbolic dynamics.
- A subshift is a pair (X;˙) where X is a closed and ˙-invariant subset of some AZ. To conserve notation, we will often refer to the subshift (X;˙) as simply X. A subshift Xis transitive if there exists x2Xsuch that X= O(x), the closure of the orbit O(x) = f˙n(x): n2Zg. We call such a point x2Xa transitive point.
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