3 papers
math.MG2025
On the uniformity and size of microsets
Richárd Balka, Vilma Orgoványi, Alex Rutar
We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set with Assouad dimen…
math.DS2025
Two-scale branching functions and inhomogeneous attractors
Vilma Orgoványi, Alex Rutar
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectru…
math.DS2024
Interior points and Lebesgue measure of overlapping Mandelbrot percolation sets
Vilma Orgoványi, Károly Simon
We consider a special one-parameter family of d-dimensional random, homogeneous self-similar iterated function systems (IFSs) satisfying the finite type condition. The object of ou…