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math.DS2024
Thermodynamic formalism of countably generated self-affine sets
Antti Käenmäki, Ian D. Morris
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earli…
math.CA2024
Level sets of prevalent Hölder functions
Roope Anttila, Balázs Bárány, Antti Käenmäki
We study the level sets of prevalent Hölder functions. For a prevalent -Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bo…
math.DS2024
Local dimension spectrum for dominated planar self-affine sets
Alex Batsis, Antti Käenmäki, Tom Kempton
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this…