Local dimension spectrum for dominated irreducible planar self-affine sets

Abstract: The local dimension spectrum gives a way to quantify fractal properties of a given measure. It is well understood for self-similar measures without overlaps. In this article we study the local dimension spectrum for dominated self-affine measures. Our main results completely characterize the behavior of the symbolic spectrum, and after detailed analysis on the exact dimensionality of self-affine measures we exhibit new deterministic results for the local dimension spectrum on a much wider range than was previously understood.