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math.DS2022
A dichotomy on the self-similarity of graph-directed attractors
Kenneth J. Falconer, Jiaxin Hu, Junda Zhang
This paper seeks conditions that ensure that the attractor of a graph directed iterated function system (GD-IFS) cannot be realised as the attractor of a standard iterated function…
math.PR2022★ 3 cited
Box-counting dimension in one-dimensional random geometry of multiplicative cascades
Kenneth J. Falconer, Sascha Troscheit
We investigate the box-counting dimension of the image of a set under a random multiplicative cascade function . The corresponding result for Hausdorff di…