On the topological pressure of random bundle transformations in sub-additive case

TL;DR

This paper extends the concept of topological pressure to sub-additive potentials within random dynamical systems, establishing a variational principle that links topological and measure-theoretic aspects.

Contribution

It introduces a new definition of topological pressure for sub-additive potentials in random systems and proves a relativized variational principle for it.

Findings

Defined topological pressure for sub-additive potentials in random systems

Proved the relativized variational principle for this pressure

Established foundational results for further research in random dynamical systems

Abstract

In this paper, we define the topological pressure for sub-additive potentials via separated sets in random dynamical systems and we give a proof of the relativized variational principle for the topological pressure.