Short, Ian
(2012).
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| DOI (Digital Object Identifier) Link: | http://doi.org/10.1090/S0002-9939-2011-11032-3 |
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| Google Scholar: | Look up in Google Scholar |
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 |
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| Copyright Holders: | 2011 American Mathematical Society |
| ISSN: | 1088-6826 |
| Keywords: | continued fractions; convergence; divergence; Hausdorff dimension; Möbius transformations; sets of divergence |
| Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 30460 |
| Depositing User: | Ian Short |
| Date Deposited: | 16 Jan 2012 09:47 |
| Last Modified: | 02 Aug 2016 22:27 |
| URI: | http://oro.open.ac.uk/id/eprint/30460 |
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