Mathematical Sciences: Topics in Dynamical Systems: Attractors, Dimension, Lattice Models

Pesin教授将研究光滑耗散动力系统中轨道的随机行为，该系统的奇点具有接近经典双曲吸引子的吸引子。目标是通过计算吸引子的尺寸特征来描述吸引子的几何结构。主要研究人员还将考虑格子模型中时空混沌的出现，该格子模型被构造为一系列强双曲动力系统。这项研究涉及随机动力系统。这些系统被用来模拟大量相互作用的粒子的行为，因此潜在的应用是重要的。Pesin教授以前的工作最近变得重要起来，因为它提供了关于系统吸引子的尺寸参数的大量信息。有迹象表明，目前的研究也将立即得到应用。

Professor Pesin will study the stochastic behavior of trajectories in smooth dissipative dynamical systems with singularities having attractors which are close to classical hyperbolic attractors. The object will be to describe the geometric structure of the attractors by calculating their dimension like characteristics. The principal investigator will also consider the appearance of space-time chaos in the lattice models which are constructed as a chain of strongly hyperbolic dynamical systems. This research involves random dynamical systems. These systems are used to model the behavior of large numbers of interacting particles and therefore the potential applications are significant. Previous work of Professor Pesin has recently become important because it gave considerable information on the dimension parameters of the attractors of the system. There is an indication that the current research will also find immediate application.