Mathematical Sciences: RUI: Asymptotics of the Lyapunov Spectrum and Stabilization by Noise

数学科学：RUI：李雅普诺夫谱的渐进性和噪声稳定性

• 批准号: 9107592
• 负责人: Volker Wihstutz
• 金额: $ 4.74万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107592&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Asymptotics; Lyapunov

The principal investigator will conduct research on several problems about the asymptotics of the Lyapunov spectrum and stabilization by noise. Lyapunov exponents of random differential equations characterize the exponential divergence of solutions to such equations. The research involves several fields of mathematics: probability, differential equations, control theory and ergodic theory, and is relevant to applied engineering problems. The specific problems are noise dependence of the p'th moment Lyapunov exponent, invariant probability measures and the Lyapunov exponents in non-Markovian situations, stabilizing effects of noise in linear and nonlinear systems, and by computer simulations numerics for estimating rotation numbers, as well as pathwise and moment, Lyapunov exponents. The principal investigator will conduct research on several problems about the asymptotics of the Lyapunov spectrum and stabilization by noise. Lyapunov exponents of random differential equations characterize the exponential divergence of solutions to such equations. The research involves several fields of mathematics: probability, differential equations, control theory and ergodic theory: and is relevant to applied engineering problems.

主要研究人员将对Lyapunov谱的渐近性和噪声稳定化等几个问题进行研究。随机微分方程解的Lyapunov指数刻画了其解的指数发散性。该研究涉及多个数学领域：概率论、微分方程、控制论和遍历理论，并与应用工程问题相关。具体问题包括p阶矩Lyapunov指数、不变概率度量和非马尔科夫情形下Lyapunov指数的噪声依赖性，噪声在线性和非线性系统中的稳定化作用，以及通过计算机模拟估计旋转数的数值，以及路径和矩、Lyapunov指数。主要研究人员将对Lyapunov谱的渐近性和噪声稳定化等几个问题进行研究。随机微分方程解的Lyapunov指数刻画了其解的指数发散性。这项研究涉及几个数学领域：概率论、微分方程、控制论和遍历理论：并与应用工程问题相关。