Dynamics of Fuchsian meromorphic connections with real periods
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913398134931456 |
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| author | Abate, Marco Rakhimov, Karim |
| author_facet | Abate, Marco Rakhimov, Karim |
| contents | In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible $ω$-limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than $-1$ and a far-reaching generalization to our case of the classical Teichmüller lemma for quadratic differentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of Fuchsian meromorphic connections with real periods Abate, Marco Rakhimov, Karim Complex Variables Dynamical Systems In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible $ω$-limit sets of simple geodesics in this case. The main tools are the study of the singular flat metric associated to the meromorphic connection, an explicit description of the geodesics nearby a Fuchsian pole with real residue larger than $-1$ and a far-reaching generalization to our case of the classical Teichmüller lemma for quadratic differentials. |
| title | Dynamics of Fuchsian meromorphic connections with real periods |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2406.13353 |