Dimensions of Bedford-McMullen type sets in ${\mathbb{Z}}^2$

Junjie Miao, Minghui Xu

We study forward orbits in ${\mathbb{Z}}^2$ generated by the expanding affine maps $(x,y)\mapsto (mx+i,ny+j)$, where $m\ge n\ge 2$ are integers and $(i,j)$ ranges over a nonempty digit…