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Conformal iterated function systems with applications to the geometry of continued fractions
Authors:R Daniel Mauldin  Mariusz Urbanski
Institution:Department of Mathematics, University of North Texas, Denton, Texas 76203 ; Department of Mathematics, University of North Texas, Denton, Texas 76203
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.

Keywords:Iterated function systems  continued fractions  Hausdorff dimension  Hausdorff and packing measures  arithmetic densities
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