An explicit formula for the pressure of box-like affine iterated function systems

Abstract

In this article we investigate the pressure function and affinity dimension for iterated function systems associated to the “box-like” self-affine fractals investigated by D.-J. Feng, Y. Wang, and J. M.‘Fraser. Combining previous results of V. Yu. Protasov, A. Käenmäki and the author we obtain an explicit formula for the pressure function which makes it straightforward to compute the affinity dimension of box-like self-affine sets. We also prove a variant of this formula which allows the computation of a modified singular value pressure function defined by J. M. Fraser. We give some explicit examples where the Hausdorff and packing dimensions of a box-like self-affine fractal may be easily computed.