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Ergodic transformations from an interval into itself. (English) Zbl 0371.28017

##### MSC:
 28D05 Measure-preserving transformations
Full Text:
##### References:
 [1] A. O. Gel$$^{\prime}$$fond, A common property of number systems, Izv. Akad. Nauk SSSR. Ser. Mat. 23 (1959), 809 – 814 (Russian). [2] A. Lasota, Invariant measures and functional equations, Aequationes Math. 9 (1973), 193 – 200. · Zbl 0269.28008 · doi:10.1007/BF01832626 · doi.org [3] A. Lasota and James A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481 – 488 (1974). · Zbl 0298.28015 [4] T. Y. Li and James A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, 985 – 992. · Zbl 0351.92021 · doi:10.2307/2318254 · doi.org [5] W. Parry, On the \?-expansions of real numbers, Acta Math. Acad. Sci. Hungar. 11 (1960), 401 – 416 (English, with Russian summary). · Zbl 0099.28103 · doi:10.1007/BF02020954 · doi.org [6] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar 8 (1957), 477 – 493. · Zbl 0079.08901 · doi:10.1007/BF02020331 · doi.org [7] S. M. Ulam, A collection of mathematical problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York-London, 1960. · Zbl 0086.24101 [8] A. A. Kosjakin and E. A. Sandler, Ergodic properties of a certain class of piecewise smooth transformations of a segment, Izv. Vysš. Učebn. Zaved. Matematika 3(118) (1972), 32 – 40 (Russian). · Zbl 0252.93028
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