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

数学科学：动力系统主题：吸引子、维度、晶格模型

• 批准号: 9102887
• 负责人: Yakov Pesin
• 金额: $ 9.75万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102887&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Dynamical; Systems

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.

Pesin教授将研究 光滑耗散动力系统的轨迹 吸引子接近经典的奇点 双曲吸引子目标是描述 通过计算吸引子的维数， 特色主要研究者还将考虑 在格子模型中出现时空混沌， 构造为强双曲动力系统链。 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 颗粒，因此潜在的应用是重要的。 Pesin教授以前的工作最近变得很重要 因为它提供了大量关于 系统吸引子的参数。有迹象 目前的研究也将立即得到应用。