Topological and symbolic dynamics

By P. Kurka. 2003

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Topological chaos: what may this mean? (2008, background): “(1) transitivity implies sensitivity, which makes the former a chaotic property among CA [40]; (2) a cellular automaton which is not sensitive has equicontinuity points [43] – this divides the family into two classes, one rather deterministic and the other rather chaotic; (3) there are no minimal CA”
On automorphism groups of low complexity subshifts (2015, background): “For instance, since any Sturmian subshift is an almost one-to-one extension of an irrational rotation on the circle (see [26]), this rotation is its maximal 1-step nilsystem, or more classically its maximal equicontinuous factor.”