Publication Date
5-2024
Date of Final Oral Examination (Defense)
3-8-2024
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department Filter
Mathematics
Department
Mathematics
Supervisory Committee Chair
John D. Clemens, Ph.D.
Supervisory Committee Member
Jens Harlander, Ph.D.
Supervisory Committee Member
Uwe Kaiser, Ph.D.
Abstract
The one-dimensional full shift over a finite set A is the collection of bi-infinite sequences of symbols in A together with the left-shift map which shifts the indexing of the sequence. A shift space is a subset of a full shift defined by a collection of forbidden blocks, i.e., finite words which are not allowed to appear. Many shift spaces arise as the set of bi-infinite walks on a labeled graph, and many dynamical systems can be encoded as shift spaces where the dynamics are replaced by the left-shift map.
We introduce shift spaces and their basic properties, then discuss the classification of 1-dimensional shift spaces, the notion of conjugacy via sliding block codes, and several conjugacy invariants. We end with some exploration into the structure of the kernel of a sliding block code and its relationship to the image shift space.
DOI
https://doi.org/10.18122/td.2245.boisestate
Recommended Citation
Miller, Jacob, "A Survey of the Classification of 1-Dimensional Shift Systems" (2024). Boise State University Theses and Dissertations. 2245.
https://doi.org/10.18122/td.2245.boisestate