Some notes on the topological pressure of non-autonomous systems

Abstract

The purpose of this note is to study the equi-continuous non-autonomous dynamical systems. We prove that the topological pressure of the system coincides with the topological pressure restricted on its non-wandering set. To prove this result, due to the lack of an appropriate variational principle for non-autonomous systems, we need to overcome some challenges. We also consider the weakly contractive iterated function systems (IFS), and find that the invariant set of the IFS plays a similar role as the non-wandering set of non-autonomous system.