On a family of self-affine sets: topology, uniqueness, simultaneous expansions

Kevin G. Hare, Nikita Sidorov

Let ${\beta }_1,{\beta }_2>1$ and $T_i(x,y)=(\frac{x+i}{{\beta }_1},\frac{y+i}{{\beta }_2}),i\in \{\pm 1\}$. Let $A:=A_{{\beta }_1,{\beta }_2}$ be the unique compact set satisfying $A = T_{1}(A) \cup T_{-1}…