A Variational Principle for the Topological Pressure of Non-autonomous Iterated Function Systems on Subsets

Motivated by the notion of topological entropy for free semigroup actions introduced by Biś, we define the Pesin--Pitskel topological pressure for non-autonomous iterated function systems via the Carathéodory--Pesin structure. We show that this Pesin--Pitskel topological pressure coincides with the corresponding weighted topological pressure. Furthermore, we establish a variational principle asserting that, for any nonempty compact subset, the Pesin--Pitskel topological pressure equals the supremum of the associated measure-theoretic pressures over all Borel probability measures supported on that subset.