Adamczewski Boris

Symbolic discrepancy and self-similar dynamics.

We consider subshifts arising from primitive substitutions, which are known to be uniquely ergodic dynamical systems. In order to precise this point, we introduce a symbolic notion of discrepancy. We show how the distribution of such a subshift is in part ruled by the spectrum of the incidence matrices associated with the underlying substitutions. We also give some applications of these results in connection with the spectral study of substitutive dynamical systems and with the arithmetical properties of some toral translations.