Regularity of Aperiodic Subshifts and Connections to Intermediate beta-Transformations
Veröffentlichungsdatum
2018-11-08
Autoren
Betreuer
Gutachter
Zusammenfassung
At the turn of this century Durand, Lagarias and Pleasants established that key features of minimal subshifts to be studied are linearly repetitive, repulsive and power free. In this thesis, we introduce generalisations and extensions of these features and establish a basic theory. Further, we study these new notions in the context of Sturmian subshifts and a family of aperiodic minimal subshifts stemming from Grigorchuk's infinite 2-group. In the second part, we study sequences of intermediate beta-transformations. Especially, we answer the question of how a sequence of corresponding normalised Parry measures converges as beta goes to one and we connect this convergence to Sturmian subshifts and the famous Thue-Morse sequence.
Schlagwörter
Aperiodic order
;
Complexity
;
Ergodic theory
;
Subshifts
;
Grigorchuk group
;
beta-Transformations
;
Sturmian sequences
Institution
Fachbereich
Dokumenttyp
Dissertation
Zweitveröffentlichung
Nein
Sprache
Englisch
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00106948-1.pdf
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850.79 KB
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Adobe PDF
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