Affine interval exchange maps with a singular conjugacy to an IET
We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism h of [0,1] which is C0 but not C1 and such that the pull-back of the Lebesgue measure is a singular invariant mea...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| 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:2072/484502 |
| Acceso en línea: | http://hdl.handle.net/2072/484502 |
| Access Level: | acceso abierto |
| Palabra clave: | Affine interval exchange transformations Interval exchange maps 51 |
| Sumario: | We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism h of [0,1] which is C0 but not C1 and such that the pull-back of the Lebesgue measure is a singular invariant measure for the AIET. In particular, we show that for almost every IET T0 of d ≥ 2 intervals and any vector ω belonging to the central-stable space Ecs(T0), for the Rauzy-Veech renormalization, any AIET T with log-slopes given by ω and semi-conjugated to T0 is topologically conjugated to T. In addition, if ω ∉ Es (T0), the conjugacy between T and T0 is singular. |
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