Ergodic properties of infinite extension of symmetric interval exchange transformations
We prove that skew products with the cocycle given by the function f(x) = a(x − 1/2) with a ̸= 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 uniq...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/484500 |
| Online Access: | http://hdl.handle.net/2072/484500 |
| Access Level: | Open access |
| Keyword: | Interval exchange transformations Ergodicity of systems preserving infinite measures 51 |
| Summary: | We prove that skew products with the cocycle given by the function f(x) = a(x − 1/2) with a ̸= 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 cocycle given by f have infinite ergodic index. |
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