Return words in the Thue-Morse and other sequences
Résumé
We present three simple ideas which enable to determine easily the number of return words in some infinite words. Using these ideas, we give a new and very short proof of the fact that each factor of an Arnoux-Rauzy word of order $m$ has exactly $m$ return words. We describe the structure of return words for the Thue-Morse sequence and focus on infinite words which are associated to simple Parry numbers.