Non-ergodic interval exchange transformations |
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| Authors: | Michael Keane |
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| Affiliation: | 1. Faculté des Sciences, Université de Rennes, B. P. 25A, 35031, Rennes Cedex, France
2. The Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel
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| Abstract: | We 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 assumptions. |
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