Talk:Interval exchange transformation

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Cornfeld Fomin and Sinai's book gives a general construction of IET with n ergodic measures (I think there construction requires 2n+1 intervals.) Michael Keane's Non-ergodic interval exchange transformations, gives a non-uniquelly ergodic minimal 4 IET. (Keynes and Newton gave a non-uniquelly ergodic 5 IET based on an older example of W. Veech) Veech's proof that a.e. IET w/ irreducible permutation is uniquelly ergodic is in The Metric Theory of interval exchange transformations Masur's is in Interval exchange transformations and measured foliation. The bound for ergodic measure of an n interval IET is in Cornfeld Fomin and Sinai. For minimal IET's [n/2] is a bound as shown by Veech in Interval exchange transformations. Anatole Katok I think also have showed this.