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 Metric theorem and Hausdorff dimension on recurrence rate of Laurent series Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 157-171 https://doi.org/10.4134/BKMS.2014.51.1.157Printed January 1, 2014 Xue-hai Hu, Bing Li, and Jian Xu Huazhong Agricultural University, South China University of Technology, Huazhong University of Science and Technology Abstract : We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let $E_{\alpha,\beta}$ be the set of points with lower and upper recurrence rates $\alpha$, $\beta$ ($0\leq \alpha \leq \beta\leq \infty$), we prove that all the sets $E_{\alpha,\beta}$ are of full Hausdorff dimension. Then the recurrence sets $E_{\alpha,\beta}$ have constant multifractal spectra. Keywords : recurrence rate, pointwise dimension, continued fractions, Laurent series, Hausdorff dimension MSC numbers : 28A80 Downloads: Full-text PDF