Homogeneous bi-Hamiltonian structures and integrable contact systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918213979209728 |
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| author | Colombo, Leonardo de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier |
| author_facet | Colombo, Leonardo de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier |
| contents | Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator relating both Poisson structures. We show that the recursion operator relating two compatible Jacobi structures cannot produce a maximal set of functions in involution. However, as we illustrate with an example, bi-Hamiltonian structures can still be used to obtain a maximal set of functions in involution on a contact manifold, at the cost of symplectisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogeneous bi-Hamiltonian structures and integrable contact systems Colombo, Leonardo de León, Manuel Irazú, María Emma Eyrea López-Gordón, Asier Mathematical Physics Symplectic Geometry 37J35, 37J55, 70H06 Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator relating both Poisson structures. We show that the recursion operator relating two compatible Jacobi structures cannot produce a maximal set of functions in involution. However, as we illustrate with an example, bi-Hamiltonian structures can still be used to obtain a maximal set of functions in involution on a contact manifold, at the cost of symplectisation. |
| title | Homogeneous bi-Hamiltonian structures and integrable contact systems |
| topic | Mathematical Physics Symplectic Geometry 37J35, 37J55, 70H06 |
| url | https://arxiv.org/abs/2502.17269 |