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A note on stronger forms of sensitivity for inverse limit dynamical systems. (English) Zbl 1343.54010
Summary: In this paper we study stronger forms of sensitivity for inverse limit dynamical system which is induced from dynamical system on a compact metric space. We give the implication of stronger forms of sensitivity between inverse limit dynamical systems and original systems. More precisely, the inverse limit system is syndetically sensitive (resp. cofinitely sensitive, ergodically sensitive, multi-sensitive) if and only if original system is syndetically sensitive (resp. cofinitely sensitive, ergodically sensitive, multi-sensitive). Also, we prove that the inverse limit system is syndetically transitive if and only if original system is syndetically transitive.

MSC:
54H20 Topological dynamics (MSC2010)
37B20 Notions of recurrence and recurrent behavior in dynamical systems
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