Ergodic properties of infinite dimensional dynamical systems

This project aims to study ergodic properties of infinite dimensional systems of interacting chaotic units. For example units where the dynamics is non uniformly hyperbolic. The project will focus on two types if interactions between the chaotic units. The first one considers rare but strong interactions between neighbouring units. While the second type models an average or effective interaction between all units. The goal of the project is to investigate conditions under which such infinite dimensional systems admit a unique equilibrium. Represented by a Sinai Ruelle Bowen measure to determine rates of convergence to equilibrium and to study the effect of the interaction strength on the behaviour of the system.