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Title:
Using regularity to estimate Lyapunov exponents
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Abstract:
I will discuss a new method for estimating Lyapunov exponents for hypoelliptic diffusions from below using local regularity of stationary measures on the projective bundle. For damped driven truncations of nonlinear conservative SPDE in fluctuation dissipation scaling, I will outline a general strategy for proving positivity of the top Lyapunov exponent that can be applied to Galerkin truncations of the stochastic Navier Stokes equations on T^2. I will also discuss ongoing work extending this method to the Grassmannian bundle to give information on the sum of the first k Lyapunov exponents, giving a possible strategy for estimating growth of attractor dimension from below.
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