Dimension of some non-normal continued fraction sets

• Autores: Lingmin Liao, Ji-Hua Ma, Bao-Wei Wang
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 1, 2008, págs. 215-226
• Idioma: inglés
• DOI: 10.1017/s0305004108001291
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• Resumen

  • 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.