Symbolic representation of piecewise linear functions on the unit interval and application to discrepancy (Q1314404)

Let \(D_ N^*(U)\) denote the star-discrepancy of a sequence \(U\) in the unit interval. ``Self-similar sequences'' \(U\) are known for having a small discrepancy, i.e. \(L(U) : = \lim \sup ND_ N^*(U)/ \log N\) is finite, under some additional assumptions. In this paper the author applies techniques concerning substitutions on finite alphabets and automata to prove upper bounds for \(L(U)\), in a special case of such sequences. In an appendix (by H. Faure) the best possible values for the discrepancy of van der Corput and \((n \alpha)\)-sequences are given.