Mathematical Sciences: Dynamical Systems and Smooth Ergodic Theory

数学科学：动力系统和平滑遍历理论

• 批准号: 8905546
• 负责人: Lai-Sang Young
• 金额: $ 10.58万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8905546&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Smooth

The Principal Investigator will study the role of stochastic noise to determine, in particular, whether the effects of small random perturbations can accumulate to drastically alter the long term behavior of dynamical systems. She will also investigate the relationship between the dimension of an attractor and its Lyapunov exponents, and consider generalizations of Katok's theorem concerning positive entropy and homoclinic points, to higher dimensions. Chaotic systems such as weather models have the property that small errors in the input data result in large errors in the prediction. But all realistic models must incorporate noise. The Principal Investigator will answer technical questions which focus on the effects of accumulated noise on the model's long term behavior.

主要研究者将研究随机的作用 噪声，以确定，特别是，是否影响小 随机扰动会累积起来， 动力系统的长期行为。她还将 调查的尺寸之间的关系， 吸引子及其Lyapunov指数，并考虑 Katok正熵定理的推广 和同宿点，到更高的维度。 像天气模型这样的混沌系统 输入数据中的小错误会导致 预测.但所有真实的模型都必须包含噪声。的 主要研究者将回答技术问题， 重点关注累积噪声对模型长期 长期行为