A lower bound for the diaphony of generalised van der Corput sequences in arbitrary base \(b\) (Q2893503)
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scientific article; zbMATH DE number 6048388
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A lower bound for the diaphony of generalised van der Corput sequences in arbitrary base \(b\) |
scientific article; zbMATH DE number 6048388 |
Statements
20 June 2012
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base-\(q\) expansion
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Hausdorff dimension
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non-dense orbit
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A lower bound for the diaphony of generalised van der Corput sequences in arbitrary base \(b\) (English)
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Let \(q\geq 2\) be an integer and, for \(0<c<1\), put NEWLINE\[NEWLINE F_c^q=\{x\in [0,1)\:\{q^n x\}\geq c,\;\forall ~n\geq 0\}, NEWLINE\]NEWLINE where \(\{y\}\) denotes the fractional part of the real number \(y\).NEWLINENEWLINEInspired by previous works of \textit{J. Nilsson} [Isr. J. Math. 171, 93--110 (2009; Zbl 1189.11038)] and \textit{Y. B. Pesin} [Dimension theory in dynamical systems: contemporary views and applications. Chicago: Univ. Chicago Press (1997; Zbl 0895.58033)], the author determines the Hausdorff dimension of \(F_c^q\). From the abstract: This dimension ``can be calculated using the spectral radius of the transition matrix of the corresponding subshift''.
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