On minimality of nonautonomous dynamical systems - Kolyada, S.F.; Snoha, Ľ.; Trofimchuk, S.I. (Нелінійні коливання, 2004)
The minimality of a nonautonomous dynamical system given by a compact Hausdorff space X and a sequence of continuous selfmaps of X is studied. A sufficient condition for nonminimality of such a system is formulated. A special attention is paid to the particular case when X is a real compact interval I. A sequence of continuous selfmaps of I forming a minimal nonautonomous system may uniformly converge. For instance, the limit may be any topologically transitive map. But if all the maps in the sequence are surjective then the limit is necessarily monotone. An example is given when the limit is the identity. As an application, in a simple way we construct a triangular map in the square I² with the property that every point except of those in the leftmost fibre has an orbit whose ω-limit set coincides with the leftmost fibre.