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Period doubling bifurcations for families of maps on \(R^ n\). (English) Zbl 0521.58041

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems
37D99 Dynamical systems with hyperbolic behavior
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
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[1] Collet, P.; Eckmann, J.-P., Universal Properties of Continuous Maps of the Interval to Itself, (1979), New York · Zbl 0456.58016
[2] Collet, P.; Eckmann, J.-P.; Lanford, O. E., Universal Properties of Maps on an Interval, Commun. Math. Phys., 76, 211-254, (1980) · Zbl 0455.58024
[3] Derrida, B.; Gervois, A.; Pomeau, Y., No article title, J. Phys., A12, 269, (1979)
[4] Feigenbaum, M., No article title, J. Stat. Phys., 19, 25, (1978) · Zbl 0509.58037
[5] Feigenbaum, M., No article title, Phys. Lett., 74A, 375, (1979)
[6] Franceschini, V., A Feigenbaum Sequence of Bifurcations in the Lorenz Model, J. Stat. Phys., 22, 397-406, (1980)
[7] Franceschini, V.; Tebaldi, C., Sequences of Infinite Bifurcations and Turbulence in a 5-Modes Truncation of the Navier-Stokes Equations, J. Stat. Phys., 21, 707-726, (1979)
[8] Lanford, O. E., Remarks on the Accumulation of Period-Doubling Bifurcations, (1979), New York
[9] A. Libchaber and J. Maurer, Une expérience de Rayleigh-Bénard de géométrie réduite,J. de Physique41, Colloque C3:51-56 (1980).
[10] M. Campanino, H. Epstein, and D. Ruelle, On Feigenbaum’s Functional Equation, preprint IHES; M. Campanino and H. Epstein, On the Existence of Feigenbaum’s Fixed Point,Commun. Math. Phys., to appear.
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