Average Topological Pressure and a Variational Principle

In this paper, we define a new version of topological pressure, called average topological pressure, for dynamical systems. We present some of its properties and prove an Abramov-Rokhlin-like relation using the new defined quantity. It connects the topological pressure of the skew product of a random dynamical system to the topological entropy of the noise map and the average topological pressure. The topological pressure of random dynamical systems is connected to the average topological pressure via a variational principle.