University of Oulu

Fan, A., Liao, L. & Wu, M. Math. Z. (2018) 290: 63.

Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems

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Author: Fan, Aihua1,2; Liao, Lingmin3; Wu, Meng4,5
Organizations: 1School of Mathematics and Statistics, Huazhong Normal University, 152 Luoyu Road, Wuhan 43007, China
2LAMFA, UMR 7352 CNRS, Université de Picardie, 33 Rue Saint Leu, 80039 Amiens, France
3LAMA UMR 8050 CNRS, Université Paris-Est Créteil, 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France
4Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014 Oulu, Finland
5Present Address: Einstein Institute of Mathematics, Edmond J. Safra Campus (Givat Ram), The Hebrew University, 91904 Jerusalem, Israel
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Springer Nature, 2018
Publish Date: 2019-01-10


In this paper, we study the multiple ergodic averages of a locally constant real-valued function in linear Cookie-Cutter dynamical systems. The multifractal spectrum of these multiple ergodic averages is completely determined.

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Series: Mathematische Zeitschrift
ISSN: 0025-5874
ISSN-E: 1432-1823
ISSN-L: 0025-5874
Volume: 290
Issue: 1-2
Pages: 63 - 81
DOI: 10.1007/s00209-017-2008-7
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The first author is partially supported by NSFC No. 11471132 and by the self-determined research funds of CCNU (No. CCNU14Z01002) from the basic research and operation of MOE. The third author is partially supported by Academy of Finland, the Centre of Excellence in Analysis and Dynamics Research and by the ERC starting Grant 306494.
Copyright information: © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.