Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems
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| Format: | Preprint |
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2024
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| _version_ | 1866912294346162176 |
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| author | Gutierrez-Sagredo, I. Ponte, D. Iglesias Marrero, J. C. Padrón, E. |
| author_facet | Gutierrez-Sagredo, I. Ponte, D. Iglesias Marrero, J. C. Padrón, E. |
| contents | In 1986, Albert proposed a Marsden-Weinstein reduction process for cosymplectic structures. In this paper, we present the limitations of this theory in the application of the reduction of symmetric time-dependent Hamiltonian systems. As a consequence, we conclude that cosymplectic geometry is not appropriate for this reduction. Motived for this fact, we replace cosymplectic structures by more general structures: mechanical presymplectic structures. Then, we develop Marsden-Weinstein reduction for this kind of structures and we apply this theory to interesting examples of time-dependent Hamiltonian systems for which Albert's reduction method doesn't work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_11997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems Gutierrez-Sagredo, I. Ponte, D. Iglesias Marrero, J. C. Padrón, E. Differential Geometry Mathematical Physics 53D20, 70G45, 70G65, 70H05, 70H33 In 1986, Albert proposed a Marsden-Weinstein reduction process for cosymplectic structures. In this paper, we present the limitations of this theory in the application of the reduction of symmetric time-dependent Hamiltonian systems. As a consequence, we conclude that cosymplectic geometry is not appropriate for this reduction. Motived for this fact, we replace cosymplectic structures by more general structures: mechanical presymplectic structures. Then, we develop Marsden-Weinstein reduction for this kind of structures and we apply this theory to interesting examples of time-dependent Hamiltonian systems for which Albert's reduction method doesn't work. |
| title | Mechanical presymplectic structures and Marsden-Weinstein reduction of time-dependent Hamiltonian systems |
| topic | Differential Geometry Mathematical Physics 53D20, 70G45, 70G65, 70H05, 70H33 |
| url | https://arxiv.org/abs/2411.11997 |