A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915400172699648 |
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| author | Dragović, Vladimir Gajić, Borislav Jovanović, Božidar |
| author_facet | Dragović, Vladimir Gajić, Borislav Jovanović, Božidar |
| contents | We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere $S^{n-1}$. We provide a Lax representation of the equations of motion and prove complete integrability of those systems for any $n$. The integrability is provided via first integrals of degree one and two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions Dragović, Vladimir Gajić, Borislav Jovanović, Božidar Exactly Solvable and Integrable Systems Mathematical Physics Dynamical Systems 37J35, 53D25 We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere $S^{n-1}$. We provide a Lax representation of the equations of motion and prove complete integrability of those systems for any $n$. The integrability is provided via first integrals of degree one and two. |
| title | A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Dynamical Systems 37J35, 53D25 |
| url | https://arxiv.org/abs/2506.23299 |