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Keane, Michael S.; Rauzy, Gerard

Stricte ergodicite des echanges d’intervalles. (French) Zbl 0479.28012

Math. Z. 174, 203-212 (1980).
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Cited in 8 Documents

MSC:

28D05 Measure-preserving transformations

Keywords:

interval exchange transformation; cyclic exchanges; strictly ergodic
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\textit{M. S. Keane} and \textit{G. Rauzy}, Math. Z. 174, 203--212 (1980; Zbl 0479.28012)
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References:

[1] Boldrighini, C., Keane, M., Marchetti, F.: Billiards in Polygons. Ann. Probability6, 532-540 (1978) · Zbl 0377.28014
[2] Douady: Travaux de Thurston sur les surfaces-Astérisque no 66-67. Séminaire Orsay 1979
[3] Katok, A., Zemljakov, A.: Transitivité topologique des billards dans des polygones. Mat. Zametki18, 291-300 (1975) [russe]. Trad. angl.: Math. Notes18, 760-764 (1975)
[4] Katok, A.: Interval exchange transformations and some special flows are not mixing. Preprint · Zbl 0437.28009
[5] Katok, A., Stepin, A.: Approximation en théorie ergodique. Uspehi Mat. Nauk22, 81-106 (1967) [russe]
[6] Katok, A.: Invariant measures of flows on oriented surfaces. Dokl. Akad. Nauk SSSR 211, 775-778 (1973) [russe]. Frad. angl.: Soviet. Math. Dokl.14, 1104-1108 (1973) · Zbl 0298.28013
[7] Keane, M.: Interval exchange transformations. Math. Z.141, 25-31 (1975) · Zbl 0288.28020
[8] Keane, M.: Non-ergodic interval exchange transformations. Israel J. Math.26, 188-196 (1977) · Zbl 0351.28012
[9] Keynes, H., Newton, D.: A minimal non-uniquely ergodic interval exchange transformation. Math. Z.148, 101-105 (1976) · Zbl 0308.28014
[10] Kronecker, voir Koksma: Diophantische Approximation. Berlin: Springer 1937
[11] Levitt, G.: Pantalons et feuilletages des surfaces. Preprint · Zbl 0473.57014
[12] Maier, A.: Trajectoires sur des surfaces fermées orientables. Mat. Sb.12, 71-84 (1943) [russe]
[13] Oxtoby, J.: Ergodic sets. Bull. Amer. Math. Soc.58, 116-136 (1952) · Zbl 0046.11504
[14] Rauzy, G.: Une généralisation du développment en fraction continue ? Séminaire Delange-Pisot-Poitou (1976/1977)
[15] Rauzy, G.: Echanges d’intervalles et transformations induites. Acta Arith.34, 315-328 (1979) · Zbl 0414.28018
[16] Sinai, Ja.: Introduction to Ergodic Theory. Princeton: Princeton University Press (1977)
[17] Thurston, W.: The geometry and topology of 3-manifolds. Princeton Lecture Notes · Zbl 0483.57007
[18] Veech, W.: Topological Dynamics. Bull. Amer. Math. Soc.83, 775-830 (1977) · Zbl 0384.28018
[19] Veech, W.: Interval exchange transformations. Journal d’Analyse33, 222-272 (1978) · Zbl 0455.28006
[20] Weyl, H.: Über die Gleichverteilung von Zahlen mod Eins. Math. Ann.77, 313-352 (1916) · JFM 46.0278.06
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