Interval exchange transformations: Applications of Keane's construction and disjointness

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dc.contributor.advisorBoshernitzan, Michaelen_US
dc.creatorChaika, Jonen_US
dc.date.accessioned2011-07-25T02:07:32Zen_US
dc.date.available2011-07-25T02:07:32Zen_US
dc.date.issued2010en_US
dc.description.abstractThis thesis is divided into two parts. The first part uses a family of Interval Exchange Transformations constructed by Michael Keane to show that IETs can have some particular behavior including: (1) IETs can be topologically mixing. (2) A minimal IET can have an ergodic measure with Hausdorff dimension alpha for any alpha ∈ [0,1]. (3) The complement of the generic points for Lebesgue measure in a minimal non-uniquely ergodic IET can have Hausdorff dimension 0. Note that this is a dense Gdelta set. The second part shows that almost every pair of IETs are different. In particular, the product of almost every pair of IETs is uniquely ergodic. In proving this we show that any sequence of natural numbers of density 1 contains a rigidity sequence for almost every IET, strengthening a result of Veech.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2010 CHAIKAen_US
dc.identifier.citationChaika, Jon. "Interval exchange transformations: Applications of Keane's construction and disjointness." (2010) Diss., Rice University. <a href="https://hdl.handle.net/1911/62209">https://hdl.handle.net/1911/62209</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/62209en_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.subjectApplied mathematicsen_US
dc.subjectMathematicsen_US
dc.titleInterval exchange transformations: Applications of Keane's construction and disjointnessen_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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