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 On topological entropy and topological pressure of non-autonomous iterated function systems J. Korean Math. Soc.Published online July 17, 2019 Fatemeh Helen Ghane and Javad Nazarian Sarkooh Ferdowsi University of Mashhad Abstract : In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) with countable infinite alphabet. NAIFSs differ from the usual (autonomous) iterated function systems, they are given \cite{LGMU} 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 a notion of specification property under which, the NAIFS has positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the $\ast$-expansive property for NAIFSs is introduced. We will finally 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 $\ast$-expansive property. Keywords : Non-autonomous iterated function system; Topological entropy; Topological pressure; Entropy point; Specifcation property; Nonwandering point. MSC numbers : 37D35; 37B40; 37B55; 37C60; 37A35. Full-Text :