Stochastic Twist Maps and Symplectic Diffusions
Stochastic Twist Maps and Symplectic Diffusions

Fraydoun Rezakhanlou, University of California, Berkeley
IAS Room S101
I discuss two examples of random symplectic maps in this talk. As the first example consider a stochastic twist map that is defined to be a stationary ergodic twist map on a planar strip. As a natural question, I discuss the fixed point of such maps and address a PoincareBirkhoff type theorem. As the second example I consider stochastic flows associated with diffusions and discuss those diffusions which produce symplectic maps only in average sense. Using stochastic diffusions, it is possible to derive IyerConstantin Circulation Theorem for NavierStokes Equation.