2018/06/10 by Javad Nazarian Sarkooh, Sarkooh, J. Nazarian, F.H. Ghane +1
Computer Science · Mathematics · #37A35 #37B40 #37B55 #37C25 #37C60 #37D35 #Algorithms and Data Compression #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1806.03629
openalex publication_date 2018/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given \citeLGMU by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ∗-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ∗-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ∗-expansive properties.