Symbolic discrepancy and self-similar dynamics. (Q1774095)

The author studies symbolic discrepancy for sequences and for subshifts. For infinite sequences (on finite alphabets) this quantity essentially describes how well the sequence sticks to being uniformly distributed with respect to the probability measure naturally associated with this sequence. Without entering into technical details we can comment on one of the main theorems in this paper by saying that the discrepancy of an iterative fixed point of a primitive morphism is governed (for its order of magnitude) by the second eigenvalue of the morphism and its multiplicity, but also -- in some precise cases -- by an explicit complex number depending on the morphism and on the sequence, that is not invariant by abelianization of the morphism.