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METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES
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 Title & Authors
METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES
Hu, Xue-Hai; Li, Bing; Xu, Jian;
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 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 be the set of points with lower and upper recurrence rates , (), we prove that all the sets , are of full Hausdorff dimension. Then the recurrence sets have constant multifractal spectra.
 Keywords
recurrence rate;pointwise dimension;continued fractions;Laurent series;Hausdorff dimension;
 Language
English
 Cited by
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