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 -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.