具有类碎轨性质的动力系统的若干问题

碎轨性质是双曲系统的重要性质，在动力系统研究中具有重要的应用。随着非一致双曲系统的研究，人们发现一些类似碎轨性质在平衡态理论、大偏差理论，重分形分析和万有性问题等研究中具有重要的作用。本项目主要研究具有类碎轨性质的流和amenable群作用系统的万有性，熵和平均维数的条件变分原理以及emergence理论，并注意在微分动力系统和测地流中的应用研究。本项目的研究将加深人们对动力系统复杂性的认识。

Specification property is an important property for hyperbolic systems, which has significant applications in the study of dynamical systems. With the development of the theory of non-uniformly hyperbolic systems, it has been found that some specification-like properties play crucial roles in the study of equilibrium state theory, large deviations theory, multi-fractal analysis and universality problems. In this project we will focus on the study of the universality, the conditional variational principles of entropy and mean dimension and the emergence theory for flows and amenable group actions with specification-like properties, as well as applications to differential dynamical systems and geodesic flows. This project will enable people acquire a deeper understanding for the complexity of dynamical systems.