Infinite Non-Conformal Iterated Function Systems
Dynamical Systems
2011-06-08 v2
Abstract
We consider a generalisation of the self-affine iterated function systems of Lalley and Gatzouras by allowing for a countable infinity of non-conformal contractions. It is shown that the Hausdorff dimension of the limit set is equal to the supremum of the dimensions of compactly supported ergodic measures. In addition we consider the multifractal analysis for countable families of potentials. We obtain a conditional variational principle for the level sets.
Cite
@article{arxiv.1105.3137,
title = {Infinite Non-Conformal Iterated Function Systems},
author = {Henry WJ Reeve},
journal= {arXiv preprint arXiv:1105.3137},
year = {2011}
}
Comments
37 pages