S. Ferenczi et al., SUBSTITUTION DYNAMICAL-SYSTEMS - ALGEBRAIC CHARACTERIZATION OF EIGENVALUES, Annales Scientifiques de l'Ecole Normale Superieure, 29(4), 1996, pp. 519-533
We give a necessary and sufficient condition allowing to compute expli
citly the eigenvalues of the dynamical system associated to any primit
ive substitution; this yields a simple criterion to determine wether a
substitution is weakly mixing; we apply these results to examples whe
re the matrix has two expanding and two contracting eigenvalues.