2022/06/21 by Dawoud Ahmadi Dastjerdi, Dastjerdi, Dawoud Ahmadi, Mahdi Aghaee +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2206.10511
openalex publication_date 2022/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let t=t1t2⋯ be an element of the full shift with shift map τ on a finite set of characters A and let Σ= closure \τi(t): i∈\N∪\0\\. Let ft=ft1, ∞=⋯∘ ft2∘ ft1 be a non-autonomous system over a compact metric space X where ti∈ \mathcal A . The set \Ft+=\fτi(t): i∈\N\ is called the shifted family of ft. If t is a transitive point of the full shift on \mathcal A, then by introducing a natural topology, \Ft+ is a classical IFS; otherwise, \Ft+=\fσ=fσ1, ∞: σ∈Σ\ is a generalized IFS. We will show that if ft has some various shadowing and specification properties, then this is true for fσ∈\F+t; however, this claim is not true for other properties such as transitivity, mixing and exactness. Also, if Σ is sofic and x∈ X is periodic point for some fσ∈\F+t, then there is a periodic σ'∈Σ such that x is periodic for fσ'∈\F+t.