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| Paper IPM / M / 18326 |
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| Abstract: | |
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We show that every topological factoring between two zero-dimensional dynamical systems can be represented by a sequence of morphisms between the levels of the associated ordered Bratteli diagramsâ. âConverselyâ, âwe prove that given an ordered Bratteli diagram $B$ with a continuous Vershik map on itâ, âevery sequence of morphisms between levels of $B$ and $C$â, âwhere $C$ is another ordered Bratteli diagram with continuous Vershik mapâ,
âinduces a topological factoring if and only if $B$ has a unique infinite minimal pathâ. âWe present a method of constructing various examples of ordered premorphisms between two decisive Bratteli diagrams such that the induced maps between the two Vershik systems are not topological factoringsâ. âWe provide sufficient conditions for the existence of a topological factoring from an ordered premorphismâ. âExpanding on the modelling of factoringâ, âwe generalize the Curtis--Hedlund--Lyndon theorem to represent factor maps between two zero-dimensional dynamical systems through sequences of sliding block codes.
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