Solvable Structures for Hamiltonian Systems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916672588218368 |
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| author | Kresic-Juric, Sasa Muriel, Concepcion Ruiz, Adrian |
| author_facet | Kresic-Juric, Sasa Muriel, Concepcion Ruiz, Adrian |
| contents | In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian vector fields. We derive explicit expressions for the corresponding Pfaffian forms, whose integration provides solutions to the Hamiltonian equations. We show that the upper $n$ forms give the action varibles, while the lower $n$ forms yield the angle variables of the system. This offers a novel interpretation of the Arnold--Liouville theorem in terms of solvable structures. We ilustrate the theory by deriving explicit solutions and action--angle variables for $n$ harmonic oscillators and the Calogero--Moser system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solvable Structures for Hamiltonian Systems Kresic-Juric, Sasa Muriel, Concepcion Ruiz, Adrian Mathematical Physics Dynamical Systems In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian vector fields. We derive explicit expressions for the corresponding Pfaffian forms, whose integration provides solutions to the Hamiltonian equations. We show that the upper $n$ forms give the action varibles, while the lower $n$ forms yield the angle variables of the system. This offers a novel interpretation of the Arnold--Liouville theorem in terms of solvable structures. We ilustrate the theory by deriving explicit solutions and action--angle variables for $n$ harmonic oscillators and the Calogero--Moser system. |
| title | Solvable Structures for Hamiltonian Systems |
| topic | Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2504.02189 |