×

Smooth triangular maps of type \(2^ \infty\) with positive topological entropy. (English) Zbl 0886.58044

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.

MSC:

37B99 Topological dynamics
54C70 Entropy in general topology
PDFBibTeX XMLCite
Full Text: DOI