Induced and nonlinear topological pressure for random dynamical systems

TL;DR

This paper introduces new concepts of induced and nonlinear fiber topological pressure for random dynamical systems, establishing their properties and variational principles, and extends the theory to higher dimensions.

Contribution

It defines non-averaged induced fiber pressure and nonlinear fiber pressure, characterizes their relationships with classical pressure, and extends the theory to higher-dimensional systems.

Findings

Defined non-averaged induced fiber pressure via spanning and separated sets.

Characterized induced fiber pressure as the pseudo-inverse of classical fiber topological pressure.

Proved variational principles for both induced and nonlinear fiber pressures.

Abstract

In this paper, we investigate induced and nonlinear fiber topological pressure for random dynamical systems. We define a non-averaged induced fiber pressure via spanning and separated sets, characterize it as the pseudo-inverse of the classical fiber topological pressure studied previously, and establish the corresponding variational principle. We also define the nonlinear fiber pressure and prove the associated variational principles. Finally, we extend the combined theory to the higher-dimensional setting.