Short, Ian
(2012).

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DOI (Digital Object Identifier) Link:  http://doi.org/10.1090/S000299392011110323 

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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:  10886826 
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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