Georgia Institute of Technology College of Sciences

On a smooth manifold, we consider a non-autonomous ordinary differential equation whose right side switches between finitely many smooth vector fields at random times. These switching times are exponentially distributed to guarantee that the resulting random dynamical system has the Markov property. A Hoermander-type hypoellipticity condition on a recurrent subset of the manifold is then sufficient for uniqueness and absolute continuity of the invariant measure of the Markov semigroup. The talk is based on a paper with my advisor Yuri Bakhtin.