Ergodic properties of infinite dimensional dynamical systems

本项目旨在研究由相互作用的混沌单元组成的无限维系统的遍历性质。例如，动力学为非一致双曲线的单位。该项目将专注于两种类型的混沌单元之间的相互作用。第一种观点认为相邻单位之间罕见但强烈的相互作用。而第二种类型对所有单元之间的平均或有效交互进行建模。该项目的目标是研究这种无限维系统存在唯一平衡的条件。以西奈Ruelle Bowen度量为代表，以确定收敛到平衡的速率，并研究相互作用强度对系统行为的影响。

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.