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- W3213742854 abstract "This thesis consists of three chapters including ten sections, which focus on beta-expansions, related digit frequencies, generalized Thue-Morse sequences and their relations.Chapter 1 is devoted to greedy beta-expansions and related digit frequencies. In Section 1.1, we study the distributions and numbers of full and non-full words in greedy beta-expansions. In Sections 1.2 and 1.3, by studying Bernoulli-type measures and variational formulae respectively, we obtain some exact formulae for the Hausdorff dimension of some digit frequency sets in greedy beta-expansions.Chapter 2 is devoted to general beta-expansions (not only the greedy ones) and related digit frequencies. In Section 2.1, we systematically study expansions in multiple bases, which are natural generalizations of usual expansions in one base. From Section 2.2 we return to expansions in one base and consider digit frequencies. In Section 2.2, we give three small results on the digit frequencies of general beta-expansions. In Section 2.3, we study Bernoulli-type measures in a framework similar to Section 1.2, and as an application we obtain the Hausdorff dimension of some frequency subsets of the set of univoque sequences.Chapter 3 is devoted to some generalizations of the famous Thue-Morse sequence, including their relations to beta-expansions and digit frequencies. In Section 3.1, we show that a class of generalized shifted Thue-Morse sequences is strongly related to a bifurcation phenomenon on the digit frequencies of unique beta-expansions. In Section 3.2, we study expansions of generalized Thue-Morse numbers, which are defined by further generalizations of the generalized shifted Thue-Morse sequences given in Section 3.1. Finally we consider another class of generalizations of the Thue-Morse sequence in Sections 3.3 and 3.4, and respectively we study related infinite products and generalized Koch curves." @default.
- W3213742854 created "2021-11-22" @default.
- W3213742854 creator A5050375655 @default.
- W3213742854 date "2021-06-22" @default.
- W3213742854 modified "2023-09-25" @default.
- W3213742854 title "Some results on beta-expansions and generalized Thue-Morse sequences" @default.
- W3213742854 hasPublicationYear "2021" @default.
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