The HADES seminar on Wednesday, September 17th, will be at 4:00pm in Room 732.

Speaker: Jacob Bedrossian

Abstract: In this talk we survey several recent results regarding nonlinear dynamics of stochastic differential equations. First, we discuss joint results with Alex Blumenthal, Keagan Callis, and Kyle Liss regarding the existence of stationary measures to SDEs with degenerate damping. This requires the nonlinearity to consistently pump energy from the forced modes to the damped modes. We determine sufficient conditions on the nonlinearity for this and then prove that “generic” examples of fluid-like SDEs satisfy these conditions. Second, we discuss joint results with Alex Blumenthal and Sam Punshon-Smith regarding estimating lower bounds of Lyapunov exponents and using this to prove non-uniqueness of stationary measures for SDEs with almost-surely invariant subspaces. In particular, we prove for L96 with every 3^rd mode stochastically forced that for strong forcing there is exactly 2 stationary measures — the trivial one supported only on the forced modes and a second mode which is absolutely continuous with respect to Lebesgue measure and so determines the long term dynamics of almost every initial condition.