Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913002954948608 |
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| author | Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. |
| author_facet | Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. |
| contents | We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $S^n\subset \mathbb R^{n+1}$ whose magnetic 2-form is the restriction of a constant 2-form from $\mathbb{R}^{n+1}$ is Liouville integrable. The integrals are quadratic and linear in momenta. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrability of the magnetic geodesic flow on the sphere with a constant 2-form Bolsinov, Alexey V. Konyaev, Andrey Yu. Matveev, Vladimir S. Differential Geometry Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 37J35, 70H06 We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $S^n\subset \mathbb R^{n+1}$ whose magnetic 2-form is the restriction of a constant 2-form from $\mathbb{R}^{n+1}$ is Liouville integrable. The integrals are quadratic and linear in momenta. |
| title | Integrability of the magnetic geodesic flow on the sphere with a constant 2-form |
| topic | Differential Geometry Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 37J35, 70H06 |
| url | https://arxiv.org/abs/2506.23312 |