动力系统长时间行为的相关问题研究

本项目将针对动力系统长时间行为的相关问题展开研究，包括系统的一致收敛性、Wasserstein度量下周期测度逼近速率以及轨道的分类与熵三方面的内容，具体如下：.1) 在可数离散amenable群作用下研究系统的一致收敛性问题，给出一致收敛性的等价刻画，并研究具有一致收敛性的系统的相关性质。.2) 在具有适当双曲性质的系统中，研究Wasserstein度量下周期测度逼近给定不变测度的速率。.3) 从轨道分类的角度出发，给出系统的熵的新的定义方式，并以此为工具研究熵理论的相关问题。

In this project, we mainly study the related issues of the long time behavior of the dynamic system, which.have three different topics, including the uniform convergence of the system, the approximation rate of the period measure under the Wasserstein metric, and the classification and entropy of the orbit. The details are as follows:.1) Study the uniform convergence of the system under the action of countable discrete amenable groups, give an equivalent characterization of uniform convergence, and study the related properties of systems with uniform convergence..2) In a system with appropriate hyperbolic properties, study the rate at which the period measure approaches a given invariant measure under Wasserstein metric ..3) From the point of orbit classification, give a new definition of the entropy, and use this as a tool to study the related issues of entropy theory.