University of Oulu

JÄRVENPÄÄ, E., JÄRVENPÄÄ, M., WU, M. and WU, W. (2017) ‘Random affine code tree fractals: Hausdorff and affinity dimensions and pressure’, Mathematical Proceedings of the Cambridge Philosophical Society, 162(2), pp. 367–382. doi: 10.1017/S0305004116000694.

Random affine code tree fractals : Hausdorff and affinity dimensions and pressure

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Author: Järvenpää, Esa1; Järvenpää, Maarit1; Wu, Meng1;
Organizations: 1Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland
2School of Mathematics and Statistics, Hubei University, Wuhan 430062, P.R. China; Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland
Format: article
Version: draft
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: Cambridge University Press, 2017
Publish Date: 2017-01-20


We prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer-Sloan condition or any other additional assumptions which have been essential in all the previously known results.

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Series: Mathematical proceedings of the Cambridge Philosophical Society
ISSN: 0305-0041
ISSN-E: 1469-8064
ISSN-L: 0305-0041
Volume: 162
Issue: 2
Pages: 367 - 382
DOI: 10.1017/S0305004116000694
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: We acknowledge the support of Academy of Finland, the Centre of Excellence in Analysis and Dynamics Research as well as the ICERM semester program on "Dimension and Dynamics". Wen Wu was also supported by NSFC (grant no. 11401188)
Copyright information: © Cambridge Philosophical Society 2016