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

首席研究员将对几个 关于李雅普诺夫谱的渐近性问题， 噪音稳定。 随机变量的李雅普诺夫指数 微分方程描述指数发散 这些方程的解。 这项研究涉及几个 数学领域：概率，微分方程， 控制理论和遍历理论，并适用于 工程问题。 具体问题是噪声依赖 p阶矩李雅普诺夫指数，不变概率 非马尔可夫情形下的测度和李雅普诺夫指数， 线性和非线性系统中噪声的稳定效应，以及 通过用于估计旋转数的计算机模拟数值， 以及路径和矩，李雅普诺夫指数。 首席研究员将对几个 关于李雅普诺夫谱的渐近性问题， 噪音稳定。 随机变量的李雅普诺夫指数 微分方程描述指数发散 这些方程的解。 这项研究涉及几个 数学领域：概率，微分方程， 控制理论和遍历理论：与应用有关 工程问题。

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.