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Dimension of some non-normal continued fraction sets
Published online by Cambridge University Press: 01 July 2008
Abstract
We consider certain sets of non-normal continued fractions for which the asymptotic frequencies of digit strings oscillate in one or other ways. The Hausdorff dimensions of these sets are shown to be the same value 1/2 as long as they are non-empty. An interesting example among them is the set of “extremely non-normal continued fractions” which was previously conjectured to be of Hausdorff dimension 0.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 215 - 225
- Copyright
- Copyright © Cambridge Philosophical Society 2008
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