Mathematical Sciences: Dynamical and Related Topics

所提出的研究必须用概率方法研究动力系统。更具体地说，研究者计划研究混沌动力系统的统计性质；发展非均匀双曲环境中自然不变测度存在的判据，并找到导致指数混合性质的机制。动力系统理论是对常微分方程（自治）系统的定性研究。这些系统模拟各种自然现象，如湍流、流体流动和生态系统。尽管局部相对简单，但随着时间的推移，动力系统的全局图像可能极其复杂和混乱；动力系统理论试图以系统和严谨的方式来理解这种全局的长期行为。

Young 9504863 The proposed research has to do with dynamical systems using probabilistic methods. More specifically, the investigator plans to study the statistical properties of chaotic dynamical systems; to develop criteria for the existence of natural invariant measures in nonuniform hyperbolic settings and find mechanisms that lead to exponential mixing properties. Dynamical systems theory is the qualitative study of (autonomous) systems of ordinary differential equations. These systems model various natural phenomena such as turbulence, fluid flows, and ecological systems. Although relatively simple locally, the global picture of a dynamical system over time can be extremely complicated and chaotic; dynamical systems theory seeks to understand this global long time behavior in a systematic and rigorous fashion.