Abstract
d -and d -shadowing properties were introduced by Dastjerdi and Hosseini in 2010 for generalizing the pseudo-orbit shadowing property. The aim of this paper is to investigate d -and d -shadowing properties of iteration systems and inverse limit systems. First, it is proved that for a dynamical system, the following three statements are equivalent: (1) f has d property (resp., d property); (2) f k has d property (resp., d property) for all k ∈ N ; (3) f k has d property (resp., d property) for some k ∈ N . Moreover, it is proved that a dynamical system having d property is chain mixing. Finally, we obtain that the inverse limit system ( X ∞ , f ∞ ) generated by { X i , φ i , f i } i ∞ =1 has d property (resp., d property, ergodic shadowing property) provided that every f i has d property (resp., d property, ergodic shadowing property).
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