Mathematical Sciences: Dynamical and Related Topics

9504863，这项拟议的研究与使用概率方法的动力系统有关。更具体地说，研究人员计划研究混沌动力系统的统计性质；发展在非均匀双曲环境中存在自然不变测度的准则，并找到导致指数混合性质的机制。动力系统理论是对(自治)常微分方程组系统的定性研究。这些系统模拟各种自然现象，如湍流、流体流动和生态系统。虽然在局部上相对简单，但随着时间的推移，动力系统的全球图景可能是极其复杂和混乱的；动力系统理论试图以系统和严格的方式理解这种全球长期行为。

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.