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Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber
Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber
Master's Theses
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.
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 Tβ,⍺ generates a subshift of finite type. We prove the set of ⍺ in …