Abstract
dc:description.abstract<p>Symbolic dynamics, and in particular β-expansions, are a ubiquitous tool in studying more complicated dynamical systems. Applications include number theory, fractals, information theory, and data storage.</p> <p>In this thesis we will explore the basics of dynamical systems with a special focus on topological dynamics. We then examine symbolic dynamics and β-transformations through the lens of sequence spaces. We discuss observations from recent literature about how matching (the property that the itinerary of 0 and 1 coincide after some number of iterations) is linked to when T<sub>β,⍺</sub> generates a subshift of finite type. We prove the set of ⍺ in the parameter space for which T<sub>β,⍺</sub> exhibits matching is symmetric and analyze some examples where the symmetry is both apparent and useful in finding a dense set of ⍺ for which T<sub>β,⍺</sub> generates a subshift of finite type.</p>
Degree
thesis:*- Name thesis:degree_name
- MS in Mathematics
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2022
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Zieber, Karl
- Contributors dc:contributor
-
- Erin Pearse
- Mathematics
- College of Science and Mathematics
Subjects
dc:subject × 3Identifiers
dc:identifier.*- Identifier
- 10.15368/theses.2022.90
- OAI identifier oai:identifier
- oai:digitalcommons.calpoly.edu:theses-4134