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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2507.16958 |
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| _version_ | 1866911106673410048 |
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| author | Abrams, Adam Katok, Svetlana Ugarcovici, Ilie |
| author_facet | Abrams, Adam Katok, Svetlana Ugarcovici, Ilie |
| contents | We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the group. We show that the two-dimensional natural extension (reduction map) of the boundary map has a domain of bijectivity and global attractor with a finite rectangular structure, confirming a conjecture of Don Zagier. Our work is based on the construction of a special fundamental polygon, related to the free product structure of the group, whose marking is preserved by "Teichmüller deformation." |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduction theory for Fuchsian groups with cusps Abrams, Adam Katok, Svetlana Ugarcovici, Ilie Dynamical Systems 37D40, 37E10 We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the group. We show that the two-dimensional natural extension (reduction map) of the boundary map has a domain of bijectivity and global attractor with a finite rectangular structure, confirming a conjecture of Don Zagier. Our work is based on the construction of a special fundamental polygon, related to the free product structure of the group, whose marking is preserved by "Teichmüller deformation." |
| title | Reduction theory for Fuchsian groups with cusps |
| topic | Dynamical Systems 37D40, 37E10 |
| url | https://arxiv.org/abs/2507.16958 |