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Interval exchange transformations. (English) Zbl 0455.28006
##### MSC:
 28D05 Measure-preserving transformations 54H20 Topological dynamics
##### Keywords:
interval exchange transformations
##### References:
 [1] N. Bourbaki,Algèbre, Ch. IX, Paris, Hermann, 1959. [2] N. A. Friedman,Introduction to Ergodic Theory, New York, Van Nostrand-Rheinhold, 1970. [3] H. Furstenberg,Stationary Processes and Prediction theory, Annals of Math. Studies, Princeton, 1960. [4] A. Hajian and S. Kakutani,Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc.110 (1964), 136–151. · doi:10.1090/S0002-9947-1964-0154961-1 [5] P. R. Halmos,Lectures on Ergodic Theory, Math. Soc. of Japan, 1956. [6] G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers, Oxford, Clarendon Press, 1938. [7] S. Kakutani,Induced measure preserving transformations, Proc. Imp. Acad. Tokyo19 (1943), 635–641. · Zbl 0060.27406 · doi:10.3792/pia/1195573248 [8] M. Keane,Interval exchange transformations, Math. Z.141 (1975), 25–31. · doi:10.1007/BF01236981 [9] M. Keane,Non-ergodic interval exchange transformations, Israel J. Math.26 (1977), 188–196. · Zbl 0351.28012 · doi:10.1007/BF03007668 [10] C. Boldrighini, M. Keane and F. Marchetti,Billiards in polygons, preprint, 1977. [11] H. Keynes and D. Newton,A minimal non-uniquely ergodic interval exchange transformation, Math. Z.148 (1976), 101–105. · Zbl 0308.28014 · doi:10.1007/BF01214699 [12] V. A. Rohlin,Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. (2)49 (1966), 171–240. [13] Ya. G. Sinai,Introduction to Ergodic Theory, Princeton Lecture Notes Series, Princeton University Press, 1977. [14] W. A. Veech,A Second Course in Complex Analysis, New York, Benjamin, 1967. [15] W. A. Veech,Topological dynamics, to appear in Bull. Amer. Math. Soc.