Vellekoop, Michel; Berglund, Raoul On intervals, transitivity = chaos. (English) Zbl 0886.58033 Am. Math. Mon. 101, No. 4, 353-355 (1994). It is shown that a continuous map of an interval, not necessarily closed, into itself, which is topologically mixing, must have a dense set of periodic points and show sensitive dependence on initial conditions. Reviewer: G.Swiatek (University Park) Cited in 1 ReviewCited in 79 Documents MSC: 37E99 Low-dimensional dynamical systems 54H20 Topological dynamics (MSC2010) Keywords:sensitivity to initial conditions; topological transitivity PDFBibTeX XMLCite \textit{M. Vellekoop} and \textit{R. Berglund}, Am. Math. Mon. 101, No. 4, 353--355 (1994; Zbl 0886.58033) Full Text: DOI