Residual properties and almost equicontinuity

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Stronger forms of sensitivity for dynamical systems (2007, background): “(1) It is interesting to note that any Sturmian subshift, which we have proved to be syndetically sensitive, is an almost one–one extension (see [2] for a definition and for more details) of an irrational rotation of the unit circle, which is an isometry, and any isometry is far from being sensitive”
Local entropy theory (2009, background): “We note that the existence an almost equicontinuous scattering system (X, T ) established in [3] (see also [55]) allows us to construct similar transitive examples.”
Recent development of chaos theory in topological dynamics (2015, methodology): “The first possible approach is derived from results of Akin and Glasner [4] by a combination of abstract arguments.”
Null systems and sequence entropy pairs (2003, background): “It is known [3, 17] that weak mixing is strictly stronger than scattering.”
Analogues of Auslander–Yorke theorems for multi-sensitivity (2015, background): “Note that the denseness of π(Y0) in X, used heavily in [3], is a sufficient but not”