Bailbrea, Francisco; Esquembre, Francisco; Linero, Antonio Smooth triangular maps of type \(2^ \infty\) with positive topological entropy. (English) Zbl 0886.58044 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 5, 1319-1324 (1995). Summary: We explicitly construct for any \(k\) in \(\mathbb{N}\) a \({\mathcal C}^k\)-differentiable triangular map in the square \(I^2\) with the following properties: (a) it has periodic orbits of period \(2^n\) for any \(n\) and no other periodic orbits, (b) the topological entropy is positive, and (c) the set of recurrent points contains properly the set of uniformly recurrent points. Cited in 6 Documents MSC: 37B99 Topological dynamics 54C70 Entropy in general topology Keywords:smooth triangular maps; positive topological entropy PDFBibTeX XMLCite \textit{F. Bailbrea} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 5, 1319--1324 (1995; Zbl 0886.58044) Full Text: DOI