Ergodic properties of infinite extension of symmetric interval exchange transformations
We prove that skew products with the co cycle given by the function f (x) = a(x-1/2) with a not equal 0 are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover, we prove that under an additional natural assumption...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/489312 |
| Acceso en línea: | https://hdl.handle.net/2072/489312 |
| Access Level: | acceso abierto |
| Palabra clave: | Interval exchange transformations Ergodicity of systems preserving infinite measures 51 |
| Sumario: | We prove that skew products with the co cycle given by the function f (x) = a(x-1/2) with a not equal 0 are ergodic for every ergodic symmetric IET in the base, thus giving the full characterization of ergodic extensions in this family. Moreover, we prove that under an additional natural assumption of unique ergodicity on the IET, we can replace f with any differentiable function with a non-zero sum of jumps. Finally, by considering weakly mixing IETs instead of just ergodic, we show that the skew products with co cycle given by f have infinite ergodic index. |
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