The structure of <inline-formula><tex-math id="M1">\begin{document}$ \omega $\end{document}</tex-math></inline-formula>-limit sets of asymptotically non-autonomous discrete dynamical systems
Abstract:We consider a discrete non-autonomous semi-dynamical system generated by a family of continuous maps defined on a locally compact metric space. It is assumed that this family of maps uniformly converges to a continuous map. Such a non-autonomous system is called an asymptotically autonomous system. We extend the dynamical system to the metric one-point compactification of the phase space. This is done via the construction of an associated skew-product dynamical system. We prove, among other things, that the om… Show more
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