The dynamical point of view of low-discrepancy sequences

Peter J. Grabner (1) , Peter Hellekalek (2) , Pierre Liardet (3)

1 Institut für Analysis und Computational Number Theory
2 Department of Mathematics of the University of Salzburg
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this overview we show by examples, how to associate certain sequences in the higher-dimensional unit cube to suitable dynamical systems. We present methods and notions from ergodic theory that serve as tools for the study of low-discrepancy sequences and discuss an important technique, cutting- and-stacking of intervals.

Mots clés: low-discrepancy sequences; b-adic integers; irregularity of distribution; discrepancy; dynamical systems

Domaines: Théorie des nombres [math.NT]; Systèmes dynamiques [math.DS]

Peter J. Grabner, Peter Hellekalek, Pierre Liardet. The dynamical point of view of low-discrepancy sequences. Uniform Distribution Theory, 2012, 7 (1), pp.11--70. ⟨hal-00871117⟩