Connectedness of planar self-affine sets associated with non-collinear digit sets
Abstract
We study the connectedness of the planar self-affine sets
T(A,D)
generated by an integer expanding matrix
A
with
|det(A)|=3
and a non-collinear digit set
D={0,v,kAv}
where
k∈Z∖{0}
and
v∈
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,D)
.