Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions

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Recent development of chaos theory in topological dynamics (2015, result): “For a systematic study and recent results, see [2, 43, 47, 59, 93, 108].”
Conceptions of Topological Transitivity (2011, background): “erfect and compact but not admitting a countable density basis — and hence not second countable and thus not metrizable — which satisﬁes DO ++. Proof. We will sketch the construction. For details see [2], p. 91. Let K be the Cantor set and A a compact space. Via the identiﬁcations (AZ)K ∼= AZ×K ∼= (”
Upper frequent hypercyclicity and related notions (2016, background): “In Akin [1] one finds an in-depth study of Furstenberg families, along with useful properties that may be imposed on them.”