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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.DS2022
Quantization dimension for self-similar measures of overlapping construction
Mrinal Kanti Roychowdhury, Karoly Simon
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open…
math.DS2022
Projections of the random Menger sponge
Károly Simon, Vilma Orgoványi
Using a similar random process to the one which yields the fractal percolation sets, starting from the deterministic Menger sponge we get the random Menger sponge. We examine its o…