# zbMATH — the first resource for mathematics

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
##### Keywords:
interval mappings; chaos; periodic points
Full Text:
##### References:
 [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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.