Fractal dimensions of continuous piecewise linear iterated function systems
Dynamical Systems
2023-02-10 v1
Abstract
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.
Cite
@article{arxiv.2302.04333,
title = {Fractal dimensions of continuous piecewise linear iterated function systems},
author = {R. D. Prokaj and P. Raith and K. Simon},
journal= {arXiv preprint arXiv:2302.04333},
year = {2023}
}