Statistical properties of randomly perturbed dynamical systems

动力系统统计性质的研究是目前遍历理论研究中最活跃的分支之一。对于确定性动力系统，这些性质已经被建立在各种类型的系统中，包括著名的洛伦兹吸引子。该项目的目标是研究当系统受到随机扰动时，这些特性中有多少会持续存在，以及随机扰动系统的统计数据如何通过未扰动系统的统计数据来近似。

The study of statistical properties in dynamical systems is currently one of the most active branches of research in ergodic theory. For deterministic dynamical systems, such properties have been established for various classes of systems, including the famous Lorenz attractor. The goal of the project is to investigate how much of such properties persist when the system is subject to random perturbations, and how the statistics of the randomly perturbed system can be approximated via the statistics of the unperturbed one.