Cocycles over interval exchange transformations and multivalued Hamiltonian flows

2010/03/09 by Jean-Pierre Conze, Conze, Jean-Pierre, Krzysztof Fraczek +1
Mathematics · #37A40 #37C40 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A40 #msc:37C40

paper · pdf · doi:10.48550/arxiv.1003.1808

45 pages, 2 figures

arxiv created 2010/03/09 · arxiv updated 2010/03/13

Abstract

We consider interval exchange transformations of periodic type and construct different classes of recurrent ergodic cocycles of dimension ≥ 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.

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