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On the existence of Feigenbaum’s fixed point. (English) Zbl 0474.58013

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
47H10 Fixed-point theorems
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[1] Campanino, M., Epstein, H., Ruelle, D.: On Feigenbaum’s functional equation (to appear) · Zbl 0513.58034
[2] Collet, P., Eckmann, J.-P.: Properties of continuous maps of the interval to itself. In: Mathematical problems in theoretical physics, Proceedings, Lausanne 1979. Berlin, Heidelberg, New York: Springer 1980 · Zbl 0456.58016
[3] Collet, P., Eckmann, J.-P.: Iterated maps on the interval as dynamical systems. Boston: Birkhaeuser 1980 · Zbl 0458.58002
[4] Collet, P., Eckmann, J.-P., Koch, H.: Period doubling bifurcations for families of maps onR n . Preprint, University of Geneva (1979) (to appear) · Zbl 0521.58041
[5] Collet, P., Eckmann, J.-P., Lanford, O.E., III: Commun. Math. Phys.76, 211–254 (1980) · Zbl 0455.58024 · doi:10.1007/BF02193555
[6] Dieudonn√©, J.: Foundations of modern analysis. New York: Academic Press 1969 · Zbl 0176.00502
[7] Feigenbaum, M.J.: J. Stat. Phys.19, 25–52 (1978) · Zbl 0509.58037 · doi:10.1007/BF01020332
[8] Feigenbaum, M.J.: J. Stat. Phys.21, 669–706 (1979) · Zbl 0515.58028 · doi:10.1007/BF01107909
[9] Feigenbaum, M.J.: The transition to aperiodic behavior in turbulent systems. Commun. Math. Phys. (to appear) · Zbl 0465.76050
[10] Krein, M.G., Rutman, M.A.: Usp. Mat. Nauk3, 1 (23), 3–95 (1948); Engl. Transl.: Functional analysis and measure theory. Am. Math. Soc., Providence 1962
[11] Lanford, O.E., III: Remarks on the accumulation of period-doubling bifurcations. In: Mathematical problems in theoretical physics, Proceedings, Lausanne 1979. Berlin, Heidelberg, New York: Springer 1980.
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