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Dimension-theoretical results for a family of generalized continued fractions

Volume 66 / 2018

Jörg Neunhäuserer Bulletin Polish Acad. Sci. Math. 66 (2018), 115-122 MSC: 11J70, 11K50, 26A18. DOI: 10.4064/ba8157-7-2018 Published online: 3 August 2018

Abstract

We find upper and lower estimates on the Hausdorff dimension of the set of real numbers which have coefficients in a generalized continued fraction expansion that are bounded by a constant. As a consequence we prove a version of Jarník’s theorem: the set of real numbers with bounded coefficients in their generalized continued fraction representation has Hausdorff dimension one.

Authors

  • Jörg NeunhäusererLeibniz Universität Hannover
    30167 Hannover, Germany
    e-mail

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