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

TL;DR

This paper introduces a new variational principle for topological pressure in non-autonomous iterated function systems, linking topological and measure-theoretic perspectives on compact subsets.

Contribution

It defines Pesin--Pitskel topological pressure for non-autonomous systems and proves its equivalence with weighted pressure and a variational principle.

Findings

Pesin--Pitskel topological pressure coincides with weighted topological pressure.

Established a variational principle relating topological and measure-theoretic pressures.

Extended the notion of topological entropy to non-autonomous iterated function systems.

Abstract

Motivated by the notion of topological entropy for free semigroup actions introduced by Bi\'s, we define the Pesin--Pitskel topological pressure for non-autonomous iterated function systems via the Carath\'eodory--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.