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\(S\)-unimodal Misiurewicz maps with flat critical points. (English) Zbl 1065.28009
Ergodic properties of \(S\)-unimodal Misiurewicz maps [M. Misiurewicz, Publ. Math., Inst. Hautes Étud. Sci. 53, 17-51 (1981; Zbl 0477.58020)] with flat critical point are studied as nonsingular transformations with respect to Lebesgue measure on the interval and as generalizations of one-dimensional maps with indifferent periodic points. This builds on work of M. Benedicks and M. Misiurewicz [Publ. Math., Inst. Hautes Étud. Sci. 69, 203-213 (1989; Zbl 0703.58030)] and H. Thunberg [Ergodic Theory Dyn. Syst. 19, No.3, 767-807 (1999; Zbl 0966.37011)].

MSC:
28D05 Measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
60F05 Central limit and other weak theorems
37E05 Dynamical systems involving maps of the interval
37A40 Nonsingular (and infinite-measure preserving) transformations
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