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

Author(s): R. Daniel Mauldin; Mariusz Urbanski
Journal: Trans. Amer. Math. Soc. 351 (1999), 4995-5025.
MSC (1991): Primary 28A80; Secondary 58F08, 58F11, 28A78
Posted: July 21, 1999
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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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Additional Information:

R. Daniel Mauldin
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: mauldin@unt.edu

Mariusz Urbanski
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: urbanski@unt.edu

DOI: 10.1090/S0002-9947-99-02268-0
PII: S 0002-9947(99)02268-0
Keywords: Iterated function systems, continued fractions, Hausdorff dimension, Hausdorff and packing measures, arithmetic densities
Received by editor(s): April 4, 1997
Posted: July 21, 1999
Additional Notes: Research supported by NSF Grant DMS-9502952
Copyright of article: Copyright 1999, American Mathematical Society

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