English

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.

Keywords

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}
}
R2 v1 2026-06-28T08:35:27.180Z