Balanced words and dynamical systems

This article is devoted to the description of all nonperiodic balanced words with $n$ different letters. A superword $W$ is called balanced if the numbers of equal letters in any two of its factors (subwords) $u_1$ and $u_2$ of equal length differ by at most 1. Balanced words are one of the possible generalizations of Sturmian words. We give a geometric interpretation of nonperiodic balanced sequences over an $n$-letter alphabet.