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Multifractal analysis for expanding interval maps with infinitely many branches


Authors: Ai-Hua Fan, Thomas Jordan, Lingmin Liao and Michał Rams
Journal: Trans. Amer. Math. Soc. 367 (2015), 1847-1870
MSC (2010): Primary 28A80; Secondary 37E05, 28A78
DOI: https://doi.org/10.1090/S0002-9947-2014-06141-2
Published electronically: September 23, 2014
MathSciNet review: 3286501
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Abstract: In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.


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Additional Information

Ai-Hua Fan
Affiliation: School of Mathematics and Statistics, Central China Normal University, 152 Luoyu Road, 430079 Wuhan, China and LAMFA UMR 6140, CNRS, Université de Picardie Jules Verne, 33, Rue Saint Leu, 80039 Amiens Cedex 1, France
Email: ai-hua.fan@u-picardie.fr

Thomas Jordan
Affiliation: School of Mathematics, The University of Bristol, University Walk, Clifton, Bristol, BS8 1TW, United Kingdom
Email: thomas.jordan@bristol.ac.uk

Lingmin Liao
Affiliation: LAMA UMR 8050, CNRS, Université Paris-Est Créteil, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France
Email: lingmin.liao@u-pec.fr

Michał Rams
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland
Email: rams@impan.pl

DOI: https://doi.org/10.1090/S0002-9947-2014-06141-2
Keywords: Multifractal analysis, Birkhoff averages, interval maps, infinitely many branches
Received by editor(s): October 13, 2011
Received by editor(s) in revised form: February 7, 2013
Published electronically: September 23, 2014
Additional Notes: The third author was partially supported by the MNiSWN grant N201 607640 (Poland).
This work was started during a conference and workshop in Warsaw in October 2010 on Fractals in Deterministic and Random Dynamics, which was funded by the EU network CODY. The research was continued in a workshop in Warwick in April 2011 on Dimension Theory and Dynamical Systems, which was funded by the EPSRC. The authors thank both workshops for their support.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.