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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2411.18920 |
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| _version_ | 1866914011965030400 |
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| author | Agapov, Sergei |
| author_facet | Agapov, Sergei |
| contents | We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method Agapov, Sergei Dynamical Systems Analysis of PDEs Differential Geometry 37J35, 53D25, 70H06, 35C05 We study Riemannian metrics on 2-surfaces with integrable geodesic flows such that an additional first integral is high-degree polynomial in momenta. This problem reduces to searching for solutions to certain quasi-linear systems of PDEs which turn out to be semi-Hamiltonian. We construct plenty of local explicit and implicit integrable examples with polynomial first integrals of degrees 3, 4, 5. Our construction is essentially based on applying the generalized hodograph method. |
| title | Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method |
| topic | Dynamical Systems Analysis of PDEs Differential Geometry 37J35, 53D25, 70H06, 35C05 |
| url | https://arxiv.org/abs/2411.18920 |