Cocycles over interval exchange transformations and multivalued Hamiltonian flows

Abstract

We consider interval exchange transformations of periodic type and construct different classes of recurrent ergodic cocycles of dimension $\ge 1$ over this special class of IETs. Then using Poincaré sections we apply this construction to obtain recurrence and ergodicity for some smooth flows on non-compact manifolds which are extensions of multivalued Hamiltonian flows on compact surfaces.

45 pages, 2 figures