A characterization of uniquely ergodic interval exchange maps in terms of the Jacobi-Perron algorithm

An interval exchange mapT satisfies the infinite distinct orbit condition if theT-orbits of theT-discontinuities are infinite and distinct. We characterize among the interval exchange maps that satisfy this condition those that are uniquely ergodic by the convergence of an associated multidimensional continued fraction in the sense of Jacobi and Perron.