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dc.contributor.advisorChairperson, Graduate Committee: Jaroslaw Kwapiszen
dc.contributor.authorBergren, Hannah Faith Sobek.en
dc.date.accessioned2016-10-27T15:37:17Z
dc.date.available2016-10-27T15:37:17Z
dc.date.issued2016en
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/9762
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.language.isoengen
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.subject.lcshTiling (Mathematics).en
dc.subject.lcshCantor sets.en
dc.titleAbstract tiling actions, expansiveness and local structureen
dc.typeDissertationen
dc.rights.holderCopyright 2016 by Hannah Faith Sobek Bergren.en
thesis.catalog.ckey3149297en
thesis.degree.committeemembersMembers, Graduate Committee: Jaroslaw Kwapisz (chairperson); Lukas Geyer; David Ayala; Kevin Wildrick; Lisa Davis.en
thesis.degree.departmentMathematical Sciences.en
thesis.degree.genreDissertationen
thesis.degree.namePhDen
thesis.format.extentfirstpage1en
thesis.format.extentlastpage131en
mus.identifier.categoryPhysics & Mathematicsen_US
mus.relation.universityMontana State University - Bozemanen_US
mus.data.thumbpage30


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