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Absolutely continuous invariant measures for one-parameter families of one-dimensional maps. (English) Zbl 0497.58017

MSC:
37A10 Dynamical systems involving one-parameter continuous families of measure-preserving transformations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
28D05 Measure-preserving transformations
37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
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[1] Ulam, S., von Neumann, J.: Bull. Am. Math. Soc.53, 1120 (1947)
[2] Bunimovič, L.A.: Mat. Zametki8, 205–216 (1970)
[3] Ruelle, D.: Commun. Math. Phys.55, 47–51 (1977) · Zbl 0362.28013 · doi:10.1007/BF01613148
[4] Bowen, R.: Commun. Math. Phys.69, 1–17 (1979) · Zbl 0421.28016 · doi:10.1007/BF01941319
[5] Jakobson, M.V.: Dokl. Akad. Nauk SSSR243, 866–869 (1978); Sov. Math. Dokl.19, 1452–1456 (1978)
[6] Misiurewicz, M.: Absolutely continuous measures for certain maps of the interval. Publ. Math. IHES (to appear) · Zbl 0477.58020
[7] Szlenk, W.: Some dynamical properties of certain differentiable mappings of an interval, Part I. Bol. Soc. Mat. Mexico (to appear) Part II, Ergodic theory and dynamical systems, Vol. II, Katok, A. (ed.). Boston: Birkhäuser 1981
[8] Ognev, A.: Metric properties of a class of maps of the interval. Mat. Zametki (1981) (to appear) · Zbl 0497.28015
[9] Ito, S., Tanaka, S., Nakada, H.: Tokyo J. Math.2, 221–239, 241–259 (1979) · Zbl 0461.28016 · doi:10.3836/tjm/1270216320
[10] Collet, P., Eckmann, J.-P.: On the abundance of aperiodic behaviour for maps of the interval. Commun. Math. Phys.73, 115–160 (1980) · Zbl 0441.58011 · doi:10.1007/BF01198121
[11] Guckenheimer, J.: Commun. Math. Phys.70, 133–160 (1979) · Zbl 0429.58012 · doi:10.1007/BF01982351
[12] Adler, R.L.: F-expansions revisited. J: Lecture Notes in Mathematics, Vol.318, pp. 1–5. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0257.28012
[13] Walters, P.: Trans. Am. Math. Soc.236, 121–153 (1978) · doi:10.1090/S0002-9947-1978-0466493-1
[14] Brolin, H.: Ark. Mat.6, 103–144 (1966) · Zbl 0127.03401 · doi:10.1007/BF02591353
[15] Kolmogorov, A.N., Fomin, S.V.: Elements of the theory of functions and of functional analysis. Moscow, 1960 · Zbl 0235.46001
[16] Ledrappier, F.: Some properties of absolutely continuous measures on an interval. Paris, Preprint, 1980 · Zbl 0487.28015
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