Random discrete groups of Möbius transformations : probabilities and limit set dimensions : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

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dc.contributor.authorO'Brien, Graeme K
dc.date.accessioned2018-04-06T00:24:28Z
dc.date.available2018-04-06T00:24:28Z
dc.date.issued2017
dc.description.abstractThis thesis addresses two areas related to the quantification of discrete groups. We study "random" groups of Möbius transformations and in particular random two-generator groups; that is, groups where the generators are selected randomly. Our intention is to estimate the likelihood that such groups are discrete and to calculate the expectation of their associated geometric and topological parameters. Computational results of the author [55] that indicate a low probability of a random group being discrete are extended and we also assess the expected Hausdorff dimension of the limit set of a discrete group. In both areas of research analytic determinations are correlated with computational results. Our results depend on the precise notion of randomness and we introduce geometrically natural probability measures on the groups of all Möbius transformations of the circle and the Riemann sphere.en_US
dc.identifier.urihttp://hdl.handle.net/10179/13008
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectMöbius transformationsen_US
dc.subjectDiscrete groupsen_US
dc.subjectResearch Subject Categories::MATHEMATICSen_US
dc.titleRandom discrete groups of Möbius transformations : probabilities and limit set dimensions : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorO'Brien, Graeme
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
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