• Hu, Xue-Hai ;
  • Li, Bing ;
  • Xu, Jian
  • Received : 2013.01.16
  • Published : 2014.01.31


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.


recurrence rate;pointwise dimension;continued fractions;Laurent series;Hausdorff dimension


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