摘要：We introduce and study some concepts of sensitivity via Furstenberg
families. A dynamical system (𝑋,𝑓) is ℱ-sensitive if there exists a positive 𝜀 such that for every 𝑥∈𝑋 and every open neighborhood 𝑈 of 𝑥 there exists 𝑦∈𝑈 such
that the pair (𝑥,𝑦) is not ℱ-𝜀-asymptotic; that is, the time set {𝑛∶𝑑(𝑓𝑛(𝑥),𝑓𝑛(𝑦))>𝜀} belongs to ℱ, where ℱ is a Furstenberg family. A dynamical system
(𝑋,𝑓) is (ℱ1, ℱ2)-sensitive if there is a positive 𝜀 such that every 𝑥∈𝑋 is a limit of points 𝑦∈𝑋 such that the pair (𝑥,𝑦) is ℱ1-proximal but not ℱ2-𝜀-asymptotic; that is, the time set {𝑛∶𝑑(𝑓𝑛(𝑥),𝑓𝑛(𝑦))<𝛿} belongs to ℱ1 for any positive 𝛿 but the time set {𝑛∶𝑑(𝑓𝑛(𝑥),𝑓𝑛(𝑦))>𝜀} belongs to ℱ2, where
ℱ1 and ℱ2 are Furstenberg families.
