Continuity of Subadditive Pressure for Self-Affine Sets

Abstract

A \textquoteleft pressure' functional $\Phi^s (T_1,\ldots ,T_N)$, defined as the limit of sums of singular value functions of products of linear mappings $(T_1,\ldots ,T_N)$, is central in analysing fractal dimensions of self-affine sets. We investigate the continuity of $\Phi^s$ with respect to the linear mappings $(T_1,\ldots ,T_N)$ which underlie the self-affine sets.