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

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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.