ITINERARIES INDUCED BY EXCHANGE OF TWO INTERVALS

Abstract

We focus on the exchange T of two intervals with an irrational slope α. For a general subinterval I of the domain of T, the first return time to I takes three values. We describe the structure of the set of return itineraries to I. In particular, we show that it is equal to {R1,R2,R1R2,Q} where Q is amicable with R1, R2 or R1R2.