R. Daniel Prokaj and Karoly Simon
Special Families of Piecewise Linear Iterated Function Systems  
Dynamic Systems and Applications 34 (2025)   99-115

https://doi.org/10.46719/dsa2025.34.05

ABSTRACT.
In this paper, we investigate the dimension theory of some familes 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.

AMS (MOS) Subject Classification. 28A80, 37E05

Key Words and Phrases. Piecewise linear iterated function systems, Hausdorff dimension