Centralizers and Conjugacy Classes in the Group of Interval Exchange Transformations

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dc.contributor.advisorBoshernitzan, Michaelen_US
dc.creatorBernazzani, Danielen_US
dc.date.accessioned2019-05-17T15:15:29Zen_US
dc.date.available2019-05-17T15:15:29Zen_US
dc.date.created2018-05en_US
dc.date.issued2018-04-18en_US
dc.date.submittedMay 2018en_US
dc.date.updated2019-05-17T15:15:29Zen_US
dc.description.abstractWe study the group G of interval exchange transformations. Firstly, we will classify, up to conjugation in G, those interval exchange transformations which arise as towers over rotations. Secondly, expanding on previous work of Novak and Li, we will classify, up to conjugation in G, minimal interval exchange transformations which exhibit bounded discontinuity growth. As an application of this classification, we will prove that no infinite order interval exchange transformation could be conjugate in G to one of its proper powers. Thirdly, we will develop broadly applicable, generic conditions which ensure that an interval exchange transformation has no roots in G and that its centralizer is torsion-free. By combining these results with a result of Novak, we will show that a typical interval exchange transformation does not commute with any interval exchange transformations other than its powers. Finally, we will completely describe the possible centralizers of a minimal three-interval exchange transformation.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationBernazzani, Daniel. "Centralizers and Conjugacy Classes in the Group of Interval Exchange Transformations." (2018) Diss., Rice University. <a href="https://hdl.handle.net/1911/105759">https://hdl.handle.net/1911/105759</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105759en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectInterval Exchange Transformationsen_US
dc.titleCentralizers and Conjugacy Classes in the Group of Interval Exchange Transformationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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