Du, Bau-Sen A chaotic function whose nonwandering set is the Cantor ternary set. (English) Zbl 0592.26007 Proc. Am. Math. Soc. 92, 277-278 (1984). For the mapping \(f(x)=-3x+1\) for \(x\in [0,1/3]\), \(f(x)=0\) for \(x\in [1/3,2/3]\) and \(f(x)=3x-2\) for \(x\in [2/3,1]\) the author shows that the nonwandering set is the Cantor set and characterizes the periodic points and recurrent points of f using their ternary expansions. Reviewer: J.Smítal MSC: 26A18 Iteration of real functions in one variable 54H20 Topological dynamics (MSC2010) 37Cxx Smooth dynamical systems: general theory Keywords:nonwandering set; Cantor ternary set; chaotic function in the sense; of Li and Yorke × Cite Format Result Cite Review PDF Full Text: DOI References: [1] W. A. Coppel, Maps on the interval, IMA Preprint Series, No. 26, University of Minnesota, 1983. [2] Bau Sen Du, Are chaotic functions really chaotic?, Bull. Austral. Math. Soc. 28 (1983), no. 1, 53 – 66. · Zbl 0541.26002 · doi:10.1017/S0004972700026113 [3] Frederick J. Fuglister, A note on chaos, J. Combin. Theory Ser. A 26 (1979), no. 2, 186 – 188. · Zbl 0413.54012 · doi:10.1016/0097-3165(79)90068-2 [4] Peter E. Kloeden, Chaotic difference equations are dense, Bull. Austral. Math. Soc. 15 (1976), no. 3, 371 – 379. · Zbl 0335.39001 · doi:10.1017/S0004972700022802 [5] T. Y. Li and James A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), no. 10, 985 – 992. · Zbl 0351.92021 · doi:10.2307/2318254 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.