Random affine code tree fractals: Hausdorff and affinity dimensions and pressure
Dynamical Systems
2016-07-27 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1510.02827,
title = {Random affine code tree fractals: Hausdorff and affinity dimensions and pressure},
author = {Esa Järvenpää and Maarit Järvenpää and Meng Wu and Wen Wu},
journal= {arXiv preprint arXiv:1510.02827},
year = {2016}
}
Comments
16 pages, 2 figures