On three definitions of chaos (Q2755701)

At present there are several definitions of chaos based on very different backgrounds and levels of mathematical sophistication. Therefore a priori it is not obvious how these notions of chaos relate to each other and whether there is a chance that -- in the long run -- a universally accepted definition of chaos might evolve. NEWLINENEWLINENEWLINEThe authors make an attempt to solve this question by picking out three of the most popular definitions of chaos due to \textit{T. Y. Li} and \textit{J. A. Yorke} [Am. Math. Mon. 82, 985-992 (1975; Zbl 0351.92021)], \textit{L. Block} and \textit{W. A. Coppel} [Dynamics in one dimension. Lect. Notes Math. 1513, Springer Berlin (1992; Zbl 0746.58007)], and \textit{R. L. Devaney} [An introduction to chaotic dynamical systems, 2nd ed., Addison-Wesley (1989; Zbl 0695.58002)]. They show, in particular, that in the case of continuous maps on a compact interval the notions of chaos in the sense of Block and Coppel and Devaney are equivalent while each of these is sufficient but not necessary for chaos in the sense of Li and Yorke.