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Universal properties of maps on an interval. (English) Zbl 0455.58024


MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37G99 Local and nonlocal bifurcation theory for dynamical systems
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[1] Collet, P., Eckmann, J.-P.: A renormalization group analysis of the hierarchical model in statistical physics. Lecture Notes in Physics, Vol. 74. Berlin, Heidelberg, New York: Springer 1978
[2] Dieudonné, J.: Foundations of modern analysis. New York, London: Academic Press 1969 · Zbl 0176.00502
[3] Feigenbaum, M.: Quantitative universality for a class of nonlinear transformations. J. Stat. Phys.19, 25 (1978);21, 669 (1979) · Zbl 0509.58037 · doi:10.1007/BF01020332
[4] Guckenheimer, J.: Bifurcations of dynamical systems. C.I.M.E. Lectures 1978 · Zbl 0451.58025
[5] Hartmann, P.: Ordinary differential equations. New York, London: Wiley 1964
[6] Hirsch, M.W., Pugh, C.C., Shub, M.: Invariant manifolds. Lecture Notes in Mathematics, Vol. 583. Berlin, Heidelberg, New York: Springer 1977 · Zbl 0355.58009
[7] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601
[8] Lanford III, O.E.: To appear, and Lecture Notes in Physics, Vol. 116, Berlin, Heidelberg, New York: Springer 1980
[9] May, R.M.: Simple mathematical models with very complicated dynamics. Nature261, 259–467 (1976) · Zbl 1369.37088 · doi:10.1038/261459a0
[10] Misiurewicz, M.: Structure of mappings of the interval with zero entropy. Preprint I.H.E.S. (1978) · Zbl 0376.54019
[11] Misiurewicz, M.: Absolutely continuous measures for certain maps on an interval. Preprint I.H.E.S./M/79/293 (1979) · Zbl 0415.28015
[12] Singer, D.: Stable orbits and bifurcations of maps of the interval. S.I.A.M. J. Appl. Math.35, 260–267 (1978) · Zbl 0391.58014 · doi:10.1137/0135020
[13] Stefan, P.: A theorem of Sharkovskii on the existence of periodic orbits of continuous endomorphisms of the real line. Commun. Math. Phys.54, 237–248 (1977) · Zbl 0354.54027 · doi:10.1007/BF01614086
[14] Collet, P., Eckmann, J.-P.: Iterated maps on the interval as dynamical systems. Progress in Physics. Birkh äuser Boston 1980 (to appear) · Zbl 0465.58018
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