On the packing dimension of box-like self-affine sets in the plane

We consider a class of planar self-affine sets which we call 'box-like'. A box-like self-affine set is the attractor of an iterated function system (IFS) consisting of contracting affine maps which take the unit square, [0, 1]², to a rectangle with sides parallel to the axes. This class contains the Bedford–McMullen carpets and the generalizations thereof considered by Lalley–Gatzouras, Barański and Feng–Wang as well as many other sets. In particular, we allow the mappings in the IFS to have non-trivial rotational and reflectional components. Assuming a rectangular open set condition, we compute the packing and box-counting dimensions by means of a pressure type formula based on the singular values of the maps.