Thomas Jordan

Multifractal analysis for self-affine measures on Gatzouras-Lalley systems

Multifractal analysis for measures involves decomposing the support of the measure into level sets based on the local scaling behaviour (local dimension) of the measure and then looking at size (typically Hausdorff dimension of the level sets). For self-similar measures with suitable non-overlapping assumptions this is well understood and in particular the dependence on the Hausdorff dimension of the level sets on the local dimension can be shown to be analytic. We show that when looking at self-affine measures on Gatzouras-Lalley carpets, which is one of the simplest families of self-affine but not self-similar measures, much wilder behaviour can be obtained. We will show how discontinuities can be found but also assumption under which the behaviour is very similar to the self-similar case. This is joint work with István Kolossváry (Renyi Institute) and Alex Rutar (British Columbia).