Topological entropy for non-autonomous iterated function systems

Abstract

In this paper we introduce the topological entropy and the capacity topological entropies of non-autonomous iterated function systems, which extends the notion of the topological entropy of non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets, by using the Carathéodory–Pesin structure (C-P structure). We provide some properties of these notions and give the main results. In fact we give lower and upper estimations of the topological entropy of non-autonomous iterated function systems action by local entropies.