Partial separability and symplectic-Haantjes manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929412142792704 |
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| author | Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio |
| author_facet | Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio |
| contents | A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry.
As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) which allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algebra.
We also introduce a novel class of Hamiltonian systems, characterized by the existence of a generalized Stäckel matrix, which by construction are partially separable. They widely generalize the known families of partially separable Hamiltonian systems. Our systems can be described in terms of semisimple but non-maximal-rank symplectic-Haantjes manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06844 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partial separability and symplectic-Haantjes manifolds Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio Mathematical Physics Symplectic Geometry 37J35, 53A45, 70H20 A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) which allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algebra. We also introduce a novel class of Hamiltonian systems, characterized by the existence of a generalized Stäckel matrix, which by construction are partially separable. They widely generalize the known families of partially separable Hamiltonian systems. Our systems can be described in terms of semisimple but non-maximal-rank symplectic-Haantjes manifolds. |
| title | Partial separability and symplectic-Haantjes manifolds |
| topic | Mathematical Physics Symplectic Geometry 37J35, 53A45, 70H20 |
| url | https://arxiv.org/abs/2305.06844 |