Dimension-theoretical results for a family of generalized continued fractions
Tom 66 / 2018
Bulletin Polish Acad. Sci. Math. 66 (2018), 115-122 MSC: 11J70, 11K50, 26A18. DOI: 10.4064/ba8157-7-2018 Opublikowany online: 3 August 2018
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.