A characterization of zero topological entropy for a class of triangular mappings.
The paper gives a characterization of triangular maps \(F(x,y)=(f(x),g(x,y))\) of the unit square with basis map \(f\) having a closed set of periodic points. Such maps necessarily have zero topological entropy. Similar characterization of zero entropy is well-known in the case of continuous maps of the unit interval [see \textit{A. N. Sharkovsky}, \textit{S. F. Kolyada}, \textit{A. G. Sivak} and \textit{V. V. Fedorenko}, Dynamics of one-dimensional maps Mathematics and its Applications. 407. Dordrecht (1997; Zbl 0881.58020)]. It is also known that in the general case for triangular maps the same is not possible even in a particular case of triangular maps non-decreasing on the fibres.
periodic, recurrent and uniformly recurrent points
scientific article; zbMATH DE number 2022074
scientific article