Special families of piecewise linear iterated function systems
Dynamical Systems
2022-12-20 v1
Abstract
This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained from the most natural covering system. We also prove that for Lebesgue typical parameters, the 1-dimensional Lebesgue measure of the underlying attractor is positive, if this number is bigger than 1 and all the contraction ratios are positive.
Cite
@article{arxiv.2212.09378,
title = {Special families of piecewise linear iterated function systems},
author = {R. D. Prokaj and K. Simon},
journal= {arXiv preprint arXiv:2212.09378},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2103.10772