We study the connectedness of the planar self-affine sets $T(A,{ \mathcal{ D}})$ generated by an integer expanding matrix $A$ with $|\det(A)|=3$ and a non-collinear digit set ${ \mathcal D}=\{ 0, v, kAv\}$ where $k\in { \mathbb Z}\setminus\{ 0\}$ and $v\in { \mathbb Z}^2$ such that $\{ v, Av\}$ is linearly independent. By checking the characteristic polynomials of $A$ case by case, we obtain a criterion concerning only $k$ to determine the connectedness of $T(A,{ \mathcal{ D}})$.
Categories: math.GN math.GT