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.

DOI: https://doi.org/10.1090/S0002-9939-2011-11032-3

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 30460
• Item Type
• Journal Item
• ISSN
• 1088-6826
• Keywords
• continued fractions; convergence; divergence; Hausdorff dimension; Möbius transformations; sets of divergence
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2011 American Mathematical Society
• Depositing User
• Ian Short