Trajectories of chaotic interval maps (Q2800399)

The author proves that if \((x_n)_{n\in \mathbb{N}}\) is any sequence of numbers in the unit interval \([0,1]\) with the property that there is a map \(x_n\longmapsto x_{n+1}\) which is uniformly continuous on the set \(X=\{ x_n:n\in \mathbb{N} \}\), then, under certain conditions on \(X\), and after extending the map to the closure \(\overline{X}\), there exists a chaotic map of \([0,1]\) for which the given sequence is a trajectory.NEWLINENEWLINEThe notion of chaos used in the article is in the sense of \textit{R. L. Devaney} [An introduction to chaotic dynamical systems. 2nd ed. Redwood City, CA etc.: Addison-Wesley Publishing Company, Inc. (1989; Zbl 0695.58002)].NEWLINENEWLINEThe author also shows sequences which appear as trajectories of maps of \([0,1]\), but not as trajectories of chaotic maps.