Abstract
This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system (lim⟵(X,f),σf) of a dynamical system (X,f) is ℱ-transitive (resp., ℱ-mixing, (ℱ1,ℱ2)-everywhere chaotic) if and only if the system (∩n=0∞fn(X),f|∩n=0∞fn(X)) is ℱ-transitive (resp., ℱ-mixing, (ℱ1,ℱ2)-everywhere chaotic), where ℱ, ℱ1 and ℱ2 are Furstenberg families.
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