arXiv subjects

P. Raith

Publications and source records attributed to P. Raith.

2 recordsLinked to original sources

arXiv2024

Continuity of the natural dimension of piecewise linear iterated function systems

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 continuously with respect to the parameters that define the system. As an application of this property, we prove a result on the positivity of the Lebesgue measure of the attractor.

math.DS↗

arXiv2023

Fractal dimensions of continuous piecewise linear iterated function systems

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.

math.DS↗