Considering each occurrence of a word w in a recurrent
infinite word, we define the set
of return words of w to be the set of all distinct words beginning
with an occurrence of w
and ending exactly just before the next occurrence of w in the infinite
word. We give a simpler proof of the
recent result (of the second author) that an infinite word is Sturmian
if and only if each of its factors has exactly two return words in it.
Then, considering episturmian infinite words, which are a natural
generalization of Sturmian words,
we study the position of the occurrences of any factor
in such infinite words
and we determinate the return words. At last, we apply these results in
order to get a kind of balance property of
episturmian words and to calculate the recurrence function of these
words.