Talk:Interval exchange transformation

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Sources:

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.

Veech proof (1982) also works also for measured foliations as ergodicity is invariant under time change. Odiralgnirt

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.

The actual bound for interval exchanges is g where g is the genus of the associated measured foliation or translation surfaces. The original proof is by Katok ("Invariant measures of flows on orientable surfaces", Akad. Nauk SSSR 211, 1973) Odiralgnirt