We give numerical, complete invariants for topological orbit equivalence and Kakutani orbit equivalence in a class of substitution systems arising from primitive substitutions whose composition matrices have rational Perron-Frobenius eigenvalues.
"On the Topological Orbit Equivalence in a Class of Substitution Minimal Systems." Tokyo J. Math. 25 (2) 221 - 240, December 2002. https://doi.org/10.3836/tjm/1244208850