29 citations · 100 across the 28 of their papers we have counts for
35 papers
Coding multiplicity in self-similar sets on the line
Károly Simon, Jian-Ci Xiao
We study coding multiplicity for self-similar sets on the real line. When the similarity dimension exceeds one, almost every point with respect to the natural self-similar measure…
The interior of randomly perturbed self-similar sets on the line
Michel Dekking, Karoly Simon, Balazs Szekely +1
Can we find a self-similar set on the line with positive Lebesgue measure and empty interior? Currently, we do not have the answer for this question for deterministic self-similar…
Fractal dimensions of continuous piecewise linear iterated function systems
R. D. Prokaj, P. Raith, K. Simon
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…
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…
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…
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…