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

Published online by Cambridge University Press:  20 July 2016

ESA JÄRVENPÄÄ ,
MAARIT JÄRVENPÄÄ ,
MENG WU  and
WEN WU
ESA JÄRVENPÄÄ
Affiliation:
Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland. e-mails: esa.jarvenpaa@oulu.fi; maarit.jarvenpaa@oulu.fi; meng.wu@oulu.fi
MAARIT JÄRVENPÄÄ
Affiliation:
Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland. e-mails: esa.jarvenpaa@oulu.fi; maarit.jarvenpaa@oulu.fi; meng.wu@oulu.fi
MENG WU
Affiliation:
Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland. e-mails: esa.jarvenpaa@oulu.fi; maarit.jarvenpaa@oulu.fi; meng.wu@oulu.fi
WEN WU*
Affiliation:
School of Mathematics, South China University of Technology, Guangzhou 510641, P. R. China. Mathematics, P.O. Box 3000, 90014 University of Oulu, Finland. e-mail: hust.wuwen@gmail.com
*
†Corresponding author.
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 2 , March 2017 , pp. 367 - 382
Copyright
Copyright © Cambridge Philosophical Society 2016 

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