Entropy of Non-autonomous Iterated Function Systems

Abstract

The aim of this paper is to investigate the topological entropy for non-autonomous iterated function systems (NAIFSs) introduced by Ghane and Sarkooh. An inequality formula for two topological entropies with a factor map of NAIFSs is established. We extend the topological analogue of the Abramov–Rokhlin formula for the entropy of a skew product transformation. Finally, the partial variational principle is obtained about the measure-theoretic entropy and topological entropy for NAIFSs.