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Title: Criteria for Unique Ergodicity of Symbolic Dynamical Systems
Authors: Fang, Billy
Advisors: Fickenscher, Jon
Contributors: Taylor, Christine
Department: Mathematics
Class Year: 2015
Abstract: Boshernitzan proved that under certain growth conditions on the complexity function of minimal symbolic dynamical systems, there exist upper bounds for the number of ergodic measures. The proofs of these criteria are due to the ubiquity of special words in sequences of low complexity. Motivated by the goal of sharpening Boshernitzan’s bounds, we define and study the special Rauzy graph, which is a variant of the Rauzy graph that focuses on these special words. We establish properties of the special Rauzy graphs and explicitly compute them for the Morse sequence and related sequences. Finally, we describe how these graphs relate to Boshernitzan’s criteria and show how they can be used to bound the number of ergodic measures of a symbolic dynamical system.
Extent: 56 pages
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2020

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