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math.DS2024
Continuity of the natural dimension of piecewise linear iterated function systems
R. D. Prokaj, P. Raith
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. We show that typically the natural dimension of these systems changes…
math.DS2022
Special families of piecewise linear iterated function systems
R. D. Prokaj, K. Simon
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…
math.DS2021
Piecewise linear iterated function systems on the line of overlapping construction
R. D. Prokaj, K. Simon
In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of t…