The doubling property of conformal measures of infinite iterated function systems |
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Authors: | RDaniel Mauldin Mariusz Urbański |
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Institution: | Department of Mathematics, University of North Texas, Denton, TX 76203-1430, USA |
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Abstract: | We provide sufficient conditions for the conformal measures induced by regular conformal infinite iterated function systems to satisfy the doubling property. We apply these conditions to iterated function systems derived from the continued fraction algorithm—continued fractions with restricted entries. For these systems our conditions are expressed in terms of the asymptotic density properties of the allowed entries. As examples, we give some relatively large classes of sets of continued fractions with restricted entries for which the corresponding conformal measures have the doubling property. Similarly, we give some other classes for which the conformal measure does not have the doubling property. |
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Keywords: | Primary: 11A55 Secondary: 28A75 |
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