The Inverse Limit Nonautonomous Discrete Dynamical System, I
Keywords:
autonomous discrete dynamical system, bi-commutativity, closed maps, Furstenberg family, inverse limits, light maps, limit bicommutativity, nonautonomous discrete dynamical systems, open maps, perfect maps, weakly mixingAbstract
In this paper, the first dedicated by the authors to this topic, we introduce the notion of the inverse limit nonautonomous discrete dynamical system (inverse limit NDS) of an inverse sequence $\left(X_n, h_{\infty, n}\right)_n$ of nonautonomous discrete dynamical systems, which generalizes the notions of the inverse limit dynamical system and of the natural extension of an autonomous discrete dynamical system ( $X, f$ ), using the shift map of $f$ (see François Blanchard, et al. [J. Reine Angew. Math. 547 (2002), pp. 5168]. Then we start a systematic study of the inverse limit NDS, by considering both set-theoretical and topological properties.
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