2022/03/29 by Dawoud Ahmadi Dastjerdi, Dastjerdi, Dawoud Ahmadi, Mahdi Aghaee +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2203.15264
openalex publication_date 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The orbit of a point x∈ X in a classical iterated function system (IFS) can be defined as \fu(x)=fun∘⋯ ∘ fu1(x): u=u1⋯ un is a word of a full shift Σ on finite symbols and fui is a continuous self map on X \. One also can associate to σ=σ1σ2⋯∈Σ a non-autonomous system (X, fσ) where the trajectory of x∈ X is defined as x, fσ1(x), fσ1σ2(x),….Here instead of the full shift, we consider an arbitrary shift space Σ. Then we investigate basic properties related to this IFS and the associated non-autonomous systems. In particular, we look for sufficient conditions that guarantees that in a transitive IFS one may have a transitive (X, fσ) for some σ∈Σ and how abundance are such σ's.