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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2002.03684 |
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| _version_ | 1866914979156852736 |
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| author | Mettler, Thomas Paternain, Gabriel P. |
| author_facet | Mettler, Thomas Paternain, Gabriel P. |
| contents | We associate a flow $ϕ$ to a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $ϕ$ always admits a dominated splitting and identify special cases in which $ϕ$ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_03684 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Vortices over Riemann surfaces and dominated splittings Mettler, Thomas Paternain, Gabriel P. Differential Geometry Dynamical Systems We associate a flow $ϕ$ to a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $ϕ$ always admits a dominated splitting and identify special cases in which $ϕ$ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$. |
| title | Vortices over Riemann surfaces and dominated splittings |
| topic | Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2002.03684 |