Dynamical systems associated with sequences

Abstract

In this chapter, we recall elementary facts on topological dynamical systems, and we focus later on a particular case of such systems naturally associated with a bounded sequence. When the sequence takes its values in a finite set, we give an explicit characterization of the dynamical properties of the system. The last section is devoted to the spectral study of sequences with the aid of correlation measures, and to a quick survey on uniform distribution and related sets of integers. © 2010 Springer-Verlag Berlin Heidelberg.