Bulletin of the
Korean Mathematical Society BKMS

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