Conformal iterated function systems with applications to the geometry of continued fractions

@article{Mauldin1999ConformalIF,
  title={Conformal iterated function systems with applications to the geometry of continued fractions},
  author={R. Daniel Mauldin and Mariusz Urbanski},
  journal={Transactions of the American Mathematical Society},
  year={1999},
  volume={351},
  pages={4995-5025}
}
  • R. Mauldin, M. Urbanski
  • Published 21 July 1999
  • Mathematics
  • Transactions of the American Mathematical Society
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… 
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