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Hausdorff dimension of sets of divergence arising from continued fractions

Short, Ian (2012). Hausdorff dimension of sets of divergence arising from continued fractions. Proceedings of the American Mathematical Society, 140(4) pp. 1371–1385.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1090/S0002-9939-2011-11032-3
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Abstract

A complex continued fraction can be represented by a sequence of Möbius transformations in such a way that the continued fraction converges if and only if the sequence converges at the origin. The set of divergence of the sequence of Möbius transformations is equivalent to the conical limit set from Kleinian group theory, and it is closely related to the Julia set from complex dynamics. We determine the Hausdorff dimensions of sets of divergence for sequences of Möbius transformations corresponding to certain important classes of continued fractions.

Item Type: Journal Article
Copyright Holders: 2011 American Mathematical Society
ISSN: 1088-6826
Keywords: continued fractions; convergence; divergence; Hausdorff dimension; Möbius transformations; sets of divergence
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30460
Depositing User: Ian Short
Date Deposited: 16 Jan 2012 09:47
Last Modified: 04 Dec 2012 08:59
URI: http://oro.open.ac.uk/id/eprint/30460
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