Interval exchange transformations and foliations on infinite genus 2-manifolds
| Autor: | CARLOS GUTIERREZ, GILBERT HECTOR, AMÉRICO LÓPEZ |
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| Rok vydání: | 2004 |
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| Zdroj: | Ergodic Theory and Dynamical Systems. 24:1097-1108 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/s0143385704000069 |
| Popis: | For each of the following properties, there is an isometric generalized interval exchange transformation (i.e. isometric GIET) having such property: (a) non-trivial recurrence orbits are exceptional and the union of them is a dense set, moreover the intersection of the closure of two such orbits is the union of finite orbits; (b) coexistence of dense orbits and exceptional orbits; (c) existence of a dense sequence of exceptional orbits $\{\mathcal{O}(p_k)\colon k=1,2,\dotsc\}$ such that $\overline{\mathcal{O}(p_1)}\subsetneqq\overline{\mathcal{O}(p_2)}\subsetneqq\dotsb\subsetneqq\overline{\mathcal{O}(p_k)}\subsetneqq\dotsb$ . Moreover, the isometric GIET can be suspended to a smooth foliation, without singularities, on a 2-manifold. The exceptional (respectively dense) orbits of the GIET give rise to exceptional (respectively dense) leaves of the foliation. Finite genus 2-manifolds cannot support orientable foliations with the considered dynamics. |
| Databáze: | OpenAIRE |
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