Ergodic properties of infinite dimensional dynamical systems

本计画旨在研究无限维混沌系统的遍历性。例如，动力学是非一致双曲的单元。该项目将集中在两种类型，如果混沌单位之间的相互作用。第一个考虑相邻单元之间罕见但强烈的相互作用。而第二种类型的模型是所有单元之间的平均或有效的相互作用。该项目的目标是调查条件下，这种无限维系统承认一个独特的平衡。由西奈Ruelle Bowen措施，以确定收敛到平衡的速度，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.