A characterization of zero topological entropy for a class of triangular mappings
Copyright policy )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.
- University of Castile-La Mancha Spain
- Rzeszów University Poland
Topological entropy, Recurrent and uniformly recurrent points, Applied Mathematics, triangular maps, Low-dimensional dynamical systems, Topological dynamics, Triangular mappings, ECIT-89: European Conference on Iteration Theory held in Batschuns, Austria, 1989, topological entropy, Chaos, Notions of recurrence and recurrent behavior in topological dynamical systems, Discrete dynamical system, periodic, recurrent and uniformly recurrent points, Iteration of real functions in one variable, Analysis
Topological entropy, Recurrent and uniformly recurrent points, Applied Mathematics, triangular maps, Low-dimensional dynamical systems, Topological dynamics, Triangular mappings, ECIT-89: European Conference on Iteration Theory held in Batschuns, Austria, 1989, topological entropy, Chaos, Notions of recurrence and recurrent behavior in topological dynamical systems, Discrete dynamical system, periodic, recurrent and uniformly recurrent points, Iteration of real functions in one variable, Analysis
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