Leo Butler (Northwestern University)

Integrable hamiltonian systems with positive Lebesgue metric entropy.

Abstract. Examples are constructed of hamiltonian flows on Poisson manifolds which are integrable in the sense that there is an open, dense set of invariant tori on which the flow is conjugate to a translation-type flow; on the other hand, the metric entropy of the flow with respect to a canonical volume-form. It is shown that the set of invariant tori can be made arbitarily small.