Words with minimal growth function

Words of slow growth, which are a natural generalization of Sturmian words, are studied in the paper. An infinite word W = (w _n ) _n∈? is called a word of slow growth if its complexity function satisfies the relation T _W (n + 1) ? T _W (n) = 1 for all sufficiently large n. The aim of this paper is to describe all words of slow growth in terms of rotations of a circle.