Entropy stability and Milnor-Thurston invariants for Bowen-Series-like maps
We define a family of discontinuous maps on the circle, called Bowen-Series-like maps, for geometric presentations of surface groups. The family has 2N parameters, where 2N is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:326010 |
| Acceso en línea: | https://ddd.uab.cat/record/326010 https://dx.doi.org/urn:doi:10.1017/etds.2025.10245 |
| Access Level: | acceso abierto |
| Palabra clave: | Surface groups Bowen-Series maps Topological entropy Volume entropy |
| Sumario: | We define a family of discontinuous maps on the circle, called Bowen-Series-like maps, for geometric presentations of surface groups. The family has 2N parameters, where 2N is the number of generators of the presentation. We prove that all maps in the family have the same topological entropy, which coincides with the volume entropy of the group presentation. This approach allows a simple algorithmic computation of the volume entropy from the presentation only, using the Milnor-Thurston theory for one-dimensional maps. |
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