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Non-ergodic interval exchange transformations
Israel Journal of Mathematics, 1977We construct interval exchange transformations on four intervals satisfying a strong irrationality condition and having exactly two ergodic invariant probability measures. This shows that although Kronecker’s theorem remains true for interval exchange transformations, the Weyl equidistribution theorem is false even under the strongest irrationality ...
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Strict Ergodicity and Transformation of the Torus
American Journal of Mathematics, 1961Introduction. If T is a measure preserving transformation ofl a probability space Q with measure Iu, the ergodic theorem assures the existence N-1 almost everywhere with respect to /i of the average limN-'Ef(T i ), where Noo n=O f is an integrable function.
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Ergodic Theory of Random Transformations.
Journal of the American Statistical Association, 1988John C. Kieffer, Y. Kifer
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