Limit Theorems in Dynamical Systems

PI将继续他在动力系统极限定理方面的工作。主要研究方向如下：收敛到稳定律，高阶阿贝尔群作用的极限定理，随机平移的极限定理和扩散极限定理。根据确定性定律演化但在初始条件不确切时表现出随机性的系统的例子出现在从原子尺度的自然现象中（流体中粒子的布朗运动）到天文尺度（彗星和小行星的运动）。在由于随机性而不可能进行精确计算的情况下，必须使用统计描述。本提案支持的研究将通过识别相空间中对随机性负责的区域并分析这些区域中系统的行为，开发确定性系统的统计描述方法。PI还将继续他的协同活动，包括组织会议，就动态的最新进展进行讲座和小型课程，撰写调查论文并指导研究生和博士后。

The PI will continue his work on limit theorem for dynamical systems. The main directions of research will be the following: convergence to stable laws, limit theorems for actions of higher rank abelian groups, limit theorems for random translations and diffusion limit theorems.Examples of systems which evolve according to deterministic laws but exhibit stochasticity when the initial conditions are not known exactly appear in natural phenomena ranging from atomic scales (Brownian Motion of particles in fluids) to astronomical scales (motion of comets and asteroids). In cases where exact calculations are impossible due to stochasticity a statistical description has to be used. The research supported by the current proposal will develop methods of statistical description of deterministic system by identifying the regions in the phase space responsable for the stochasticity and analyzing the behaviour of the system in those regions. PI will also continue his synergistic activities including organizing conferences, giving lectures and minicourses on recent advances in dynamics, writing survey papers and mentoring graduate students and postdocs.