Conformal iterated function systems with applications to the geometry of continued fractions
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- by R. Daniel Mauldin and Mariusz Urbański PDF
- Trans. Amer. Math. Soc. 351 (1999), 4995-5025 Request permission
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.References
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Additional Information
- R. Daniel Mauldin
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: mauldin@unt.edu
- Mariusz Urbański
- Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
- Email: urbanski@unt.edu
- Received by editor(s): April 4, 1997
- Published electronically: July 21, 1999
- Additional Notes: Research supported by NSF Grant DMS-9502952
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 4995-5025
- MSC (1991): Primary 28A80; Secondary 58F08, 58F11, 28A78
- DOI: https://doi.org/10.1090/S0002-9947-99-02268-0
- MathSciNet review: 1487636