Exchange of three intervals: itineraries, substitutions and palindromicity
arXiv:1503.03376
Abstract
Given a symmetric exchange of three intervals, we provide a detailed description of the return times to a subinterval and the corresponding itineraries. We apply our results to morphisms fixing words coding non-degenerate three interval exchange transformation. This allows us to prove that the conjecture stated by Hof, Knill and Simon is valid for such infinite words.
29 pages, short version in Developments in Language Theory, 19th International Conference, DLT 2015, Liverpool, UK, July 27-30, 2015, Proceedings