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dc.contributor.authorFraser, Jonathan M.
dc.identifier.citationFraser , J M 2022 , ' The Poincaré exponent and the dimensions of Kleinian limit sets ' , The American Mathematical Monthly , vol. 129 , no. 5 , pp. 480-484 .
dc.identifier.otherPURE: 278389064
dc.identifier.otherPURE UUID: cdec1e16-376e-4b89-af51-46c97e1befb4
dc.identifier.otherJisc: 173524
dc.identifier.otherORCID: /0000-0002-8066-9120/work/110423227
dc.identifier.otherWOS: 000767660100001
dc.identifier.otherScopus: 85126474083
dc.descriptionThe author was financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Research Project Grant (RPG-2019-034).en
dc.description.abstractKleinian groups are discrete groups of isometries of hyperbolic space. Their actions give rise to intricate fractal limit sets on the boundary at infinity and there is great interest in estimating the “dimension” of these limit sets. As an invitation to this fascinating area, we provide a proof of the (well-known) result that the Poincaré exponent of a nonelementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof uses only elementary hyperbolic and fractal geometry.
dc.relation.ispartofThe American Mathematical Monthlyen
dc.rightsCopyright © 2022 The Mathematical Association of America. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectGeneral Mathematicsen
dc.subjectQA Mathematicsen
dc.titleThe Poincaré exponent and the dimensions of Kleinian limit setsen
dc.typeJournal itemen
dc.contributor.sponsorThe Leverhulme Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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