Sensitivity and property \(P\) in non-autonomous systems
In the first part of the paper, the authors provide some motivations for their work. Then they give an example of a nonautonomous system that is minimal and sensitive but not syndetically sensitive. This example is also a counterexample for the result given by \textit{T. Lu} and \textit{G. Chen} [J. Appl. Anal. Comput. 7, No. 1, 92--101 (2017; Zbl 1474.37018)] claiming that every minimal sensitive nonautonomous system is syndetically sensitive. Then the authors give sufficient conditions under which a minimal sensitive nonautonomous discrete dynamical system is syndetically sensitive (Theorem 3.3 and Theorem 3.4). In the same section, the authors also give sufficient conditions ensuring that for a topologically transitive nonautonomous system, multi-sensitivity is equivalent to thick sensitivity (Proposition 3.5). They also prove the following result: if a non-minimal nonautonomous \(M\)-system converges uniformly, then it is thickly syndetically sensitive (Theorem 3.8). The last result of the third section gives a sufficient condition under which multi-sensitivity is equivalent to thickly syndetical sensitivity (Proposition 3.13). The authors also introduce the property \(P\) for a nonautonomous dynamical system (Definition 4.1). It turns out that for nonautonomous \(M\)-systems, the property \(P\) implies multi-sensitivity, but multi-sensitivity does not imply the property \(P\). The authors also give other results about the property \(P\). One of these results says that if a nonautonomous system has the property \(P\), then it has positive topological entropy (see Theorem 4.10).
scientific article; zbMATH DE number 7259174
scientific article