Ergodicity of explicit logarithmic cocycles over IETs
We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic R-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2025 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/489105 |
| Acesso em linha: | http://hdl.handle.net/2072/489105 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Ergodicity 51 |
| Resumo: | We prove ergodicity in a class of skew-product extensions of interval exchange transformations given by cocycles with logarithmic singularities. This, in particular, provides explicit examples of ergodic R-extensions of minimal locally Hamiltonian flows with non-degenerate saddles in genus two. More generally, given any symmetric irreducible permutation, we show that for almost every choice of lengths, the skew-product built over the associated IET using a cocycle with symmetric logarithmic singularities that is odd when restricted to each of the exchanged intervals is ergodic. |
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