A result on the approximation properties of the orbit of 1 under the \(\beta\)-transformation (Q2252070)
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| Language | Label | Description | Also known as |
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| English | A result on the approximation properties of the orbit of 1 under the \(\beta\)-transformation |
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A result on the approximation properties of the orbit of 1 under the \(\beta\)-transformation (English)
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16 July 2014
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The author generalizes a previous 1-dimensional result of \textit{J. Schmeling} [Ergodic Theory Dyn. Syst. 17, No. 3, 675--694 (1997; Zbl 0908.58017)] concerning the set of bases \(\beta>1\) of the \(\beta\)-expansions of real numbers. The \(\beta\)-expansions of the real numbers were first introduced by \textit{A. Rényi} in [Acta Math. Acad. Sci. Hung. 8, 477--493 (1957; Zbl 0079.08901)].
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\(\beta\)-expansion
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Hausdorff dimension
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