In the paper, we focus on the connectedness of planar self-affine sets
T(A,D) generated by an integer expanding matrix A with ∣det(A)∣=3 and a collinear digit set D={0,1,b}v, where b>1 and
v∈R2 such that {v,Av} is linearly independent. We discuss
the domain of the digit b to determine the connectedness of
T(A,D). Especially, a complete characterization is obtained when
we restrict b to be an integer. Some results on the general case of ∣det(A)∣>3 are obtained as well.Comment: 15 pages, 10 figure