M. Hairer
On the controllability of conservative systems
(200K, pdf)

ABSTRACT.  We consider a weak form of controllability for system that have a conserved quantity and satisfy a condition of H rmander type. It is shown that such systems are approximately controllable under a weak growth condition for the conserved quantity. The proof of the result combines analytic tools with probabilistic arguments. A counterexample is given that shows that the growth condition is essential for the result to hold. Applications of the result to ergodicity questions for systems arising from non-equilibrium statistical mechanics and to the controllability of Galerkin approximations to the Euler equations are also given.