Mathematical Sciences: Dynamical Systems and Smooth Ergodic Theory

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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.