  An important question in dynamical systems is the classification problem,
i.e., the ability to distinguish between two isomorphic systems. In this work,
we study the topological factors between a family of multidimensional
substitutive subshifts generated by morphisms with uniform support. We prove
that it is decidable to check whether two minimal aperiodic substitutive
subshifts are isomorphic, under having the same combinatorial structure. The
strategy followed in this work consists of giving a complete description of the
factor maps between these subshifts. Then, we deduce some interesting
consequences on coalescence, automorphism groups, and the number of aperiodic
symbolic factors of substitutive subshifts. We also prove other combinatorial
results on these substitutions, such as the decidability of defining a
subshift, the computability of the recognizability radius, and the conjugacy
between substitutions with different supports.
