Frequency of digits in the Lüroth expansion |
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Authors: | Luis Barreira Godofredo Iommi |
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Affiliation: | a Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal b Facultad de Matemáticas, Pontificia Universidad Católica de Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Chile |
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Abstract: | In this note we consider the Lüroth expansion of a real number, and we study the Hausdorff dimension of a class of sets defined in terms of the frequencies of digits in the expansion. We also study the speed at which the approximants obtained from the Lüroth expansion converge. In addition, we describe the multifractal properties of the level sets of the Lyapunov exponent, which measures the exponential speed of approximation obtained from the approximants. Finally, we describe the relation of the Lüroth expansion with the continued fraction expansion and the β-expansion. We remark that our work is still another application of the theory of dynamical systems to number theory. |
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Keywords: | 37C45 11A67 |
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