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Cocycles over interval exchange transformations and multivalued Hamiltonian flows |
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| Authors: | Jean-Pierre Conze Krzysztof Fr?czek |
| Affiliation: | aUniversité de Rennes I, IRMAR, CNRS UMR 6625, Campus de Beaulieu, 35042 Rennes Cedex, France;bFaculty of Mathematics and Computer Science, N. Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland;cInstitute of Mathematics, Polish Academy of Science, ul. ?niadeckich 8, 00-956 Warszawa, Poland |
| Abstract: | We consider interval exchange transformations of periodic type and construct different classes of ergodic cocycles of dimension?1 over this special class of IETs. Then using Poincaré sections we apply this construction to obtain the recurrence and ergodicity for some smooth flows on non-compact manifolds which are extensions of multivalued Hamiltonian flows on compact surfaces. |
| Keywords: | MSC: 37A40 37C40 |
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