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dc.contributor.advisorChairperson, Graduate Committee: Jaroslaw Kwapiszen
dc.contributor.authorBergren, Hannah Faith Sobeken
dc.description.abstractA significant amount of literature is devoted to the study of the dynamical properties of the translation actions associated to self-affine tilings or Delone sets. A natural step is to axiomatize these essential properties among all Rd-actions on compact metric spaces. We propose a set of dynamical axioms of such an action which yields a topological conjugacy between the Rd-action and the translation action associated to a self-affine repetitive aperiodic tiling. In particular, we show that these axioms admit an expanding metric on the local cross-section of the phase space, which implies the existence of a local cross-section that is a Cantor set. We also investigate an interesting example of a tiling space that contains non-FLC tilings, which exhibits an unusually complicated local structure.en
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.subject.lcshTiling (Mathematics)en
dc.subject.lcshCantor setsen
dc.titleAbstract tiling actions, expansiveness and local structureen
dc.rights.holderCopyright 2016 by Hannah Faith Sobek Bergrenen
thesis.catalog.ckey3149297en, Graduate Committee: Lukas Geyer; David Ayala; Kevin Wildrick; Lisa Davisen Sciences.en

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