Cocycles over interval exchange transformations and multivalued Hamiltonian flows

Mathematics – Dynamical Systems

Scientific paper

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45 pages, 2 figures

Scientific paper

We consider interval exchange transformations of periodic type and construct different classes of recurrent ergodic cocycles of dimension $\geq 1$ over this special class of IETs. Then using Poincar\'e 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.

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