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Regularity of multifractal spectra of conformal iterated function systems


Authors: Johannes Jaerisch and Marc Kesseböhmer
Journal: Trans. Amer. Math. Soc. 363 (2011), 313-330
MSC (2010): Primary 37C45; Secondary 37D25, 37D35
DOI: https://doi.org/10.1090/S0002-9947-2010-05326-7
Published electronically: August 25, 2010
MathSciNet review: 2719683
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Abstract: We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is, we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we introduce the notion of regular convergence for families of cIFS not necessarily sharing the same index set, which guarantees the convergence of the multifractal spectra on the interior of their domain. In particular, we obtain an Exhausting Principle for infinite cIFS allowing us to carry over results for finite to infinite systems, and in this way to establish a multifractal analysis without the usual regularity conditions. Finally, we discuss the connections to the $ \lambda$-topology introduced by Roy and Urbański.


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Additional Information

Johannes Jaerisch
Affiliation: AG Dynamical Systems and Geometry, FB-3 Mathematik und Informatik, Universität Bremen, Bibliothekstrasse 1, 28359 Bremen, Germany
Email: jogy@math.uni-bremen.de

Marc Kesseböhmer
Affiliation: AG Dynamical Systems and Geometry, FB-3 Mathematik und Informatik, Universität Bremen, Bibliothekstrasse 1, 28359 Bremen, Germany
Email: mhk@math.uni-bremen.de

DOI: https://doi.org/10.1090/S0002-9947-2010-05326-7
Received by editor(s): February 14, 2009
Published electronically: August 25, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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