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No division implies chaos. (English) Zbl 0495.58018

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
54H20 Topological dynamics (MSC2010)
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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[1] Louis Block, Periodic orbits of continuous mappings of the circle, Trans. Amer. Math. Soc. 260 (1980), no. 2, 553 – 562. · Zbl 0497.54040
[2] Louis Block, John Guckenheimer, Michał Misiurewicz, and Lai Sang Young, Periodic points and topological entropy of one-dimensional maps, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) Lecture Notes in Math., vol. 819, Springer, Berlin, 1980, pp. 18 – 34. · Zbl 0447.58028
[3] T. Y. Li and James A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, 985 – 992. · Zbl 0351.92021
[4] Tien Yien Li, Michał Misiurewicz, Giulio Pianigiani, and James A. Yorke, Odd chaos, Phys. Lett. A 87 (1981/82), no. 6, 271 – 273.
[5] O. M. Šarkovs\(^{\prime}\)kiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. Ž. 16 (1964), 61 – 71 (Russian, with English summary).
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