ITINERARIES INDUCED BY EXCHANGE OF THREE INTERVALS

Abstract

We focus on a generalization of the three gap theorem well known in the framework of exchange of two intervals. For the case of three intervals, our main result provides an analogue of this result implying that there are at most 5 gaps. To derive this result, we give a detailed description of the return times to a subinterval and the corresponding itineraries.

Keywords

• interval exchange transformation
• three gap theorem
• return time
• first return map