Socała, Jolanta Exactness of expanding mappings. (English) Zbl 0685.28006 Ann. Pol. Math. 49, No. 1, 93-99 (1988). For a suitably defined piecewise expanding \(C^ 2\)-mapping of the d- dimensional unit cube into itself the author proves that there exists a unique absolutely continuous invariant normalized measure such that the induced dynamical system is exact. The proof is based on an idea due to A. Lasota and M. C. Mackey [Probabilistic properties of deterministic systems (1986; Zbl 0606.58002)]. For related papers see G. Keller [C. R. Acad. Sci., Paris, Sér. A 289, 625-627 (1979; Zbl 0419.28007)], M. Jabłoński [Ann. Pol. Math. 42, 185-195 (1983; Zbl 0591.28014)], D. H. Mayer [Commun. Math. Phys. 95, 1-15 (1984; Zbl 0577.58022)] and D. Candeloro [Atti Semin. Mat. Fis. Univ. Modena 35, 33-42 (1987; Zbl 0656.28008)]. Reviewer: K.Krzyżewski MSC: 28D05 Measure-preserving transformations 37A99 Ergodic theory 37D99 Dynamical systems with hyperbolic behavior 28D10 One-parameter continuous families of measure-preserving transformations Keywords:Frobenius-Perron operator; exact mapping; piecewise expanding \(C^ 2\)- mapping; absolutely continuous invariant normalized measure; dynamical system Citations:Zbl 0606.58002; Zbl 0419.28007; Zbl 0591.28014; Zbl 0577.58022; Zbl 0656.28008 PDFBibTeX XMLCite \textit{J. Socała}, Ann. Pol. Math. 49, No. 1, 93--99 (1988; Zbl 0685.28006) Full Text: DOI