Dimension-theoretical results for a family of generalized continued fractions

• Autorzy: Neunhäuserer J.

Identyfikatory

DOI

10.4064/ba8157-7-2018

• Języki publikacji: EN

Abstrakty

EN

We find upper and lower estimates on the Hausdorff dimension of the set of real numbers which have coeffcients 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 coeffcients in their generalized continued fraction representation has Hausdorff dimension one.

Słowa kluczowe

EN

generalized continued fractions; bounded coeffcients; Hausdorff dimension; Jarník's theorem

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2018
• Tom: Vol. 66, no. 2
• Strony: 115--122
• Opis fizyczny: Bibliogr. 16 poz., tab.

Twórcy

autor

Neunhäuserer J.

• Leibniz Universität Hannover, 30167 Hannover, Germany

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).