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Conformal Iterated Function Systems with Applications to the Geometry of Continued Fractions

R. Daniel Mauldin and Mariusz Urbański
Transactions of the American Mathematical Society
Vol. 351, No. 12 (Dec., 1999), pp. 4995-5025
Stable URL: http://www.jstor.org/stable/117986
Page Count: 31
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Conformal Iterated Function Systems with Applications to the Geometry of Continued Fractions
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Abstract

In this paper we obtain some results about general conformal iterated function systems. We obtain a simple characterization of the packing dimension of the limit set of such systems and introduce some special systems which exhibit some interesting behavior. We then apply these results to the set of values of real continued fractions with restricted entries. We pay special attention to the Hausdorff and packing measures of these sets. We also give direct interpretations of these measure theoretic results in terms of the arithmetic density properties of the set of allowed entries.

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