It is well known that 2-interval exchange transformation is isomorphic to the odometer transformation on some symbolic space and isomorphism is given by Ostrowski representation formula. The purpose of this paper is to extend these results to the case of 3-interval exchange transformation.
"Three-Interval Exchange Transformation and its Odometer Representation." Tokyo J. Math. 32 (2) 447 - 469, December 2009. https://doi.org/10.3836/tjm/1264170243