Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915661529219072 |
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| author | Dell'Atti, Marta Kecker, Thomas |
| author_facet | Dell'Atti, Marta Kecker, Thomas |
| contents | Some new Hamiltonian systems of quasi-Painlevé type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlevé equations, comparing the irreducible components of the inaccessible divisors arising in the blow-up process, we find bi-rational coordinate changes between some of these systems that give rise to the same global Hamiltonian structure. This scheme thus gives a method for identifying Hamiltonian systems up to bi-rational maps, which is performed in this article for systems of quasi-Painlevé type having singularities that are either square-root type algebraic poles or ordinary poles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type Dell'Atti, Marta Kecker, Thomas Classical Analysis and ODEs Mathematical Physics Algebraic Geometry Complex Variables 34M35 (primary) 34M55, 33E17, 14E15 (secondary) Some new Hamiltonian systems of quasi-Painlevé type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlevé equations, comparing the irreducible components of the inaccessible divisors arising in the blow-up process, we find bi-rational coordinate changes between some of these systems that give rise to the same global Hamiltonian structure. This scheme thus gives a method for identifying Hamiltonian systems up to bi-rational maps, which is performed in this article for systems of quasi-Painlevé type having singularities that are either square-root type algebraic poles or ordinary poles. |
| title | Geometric approach for the identification of Hamiltonian systems of quasi-Painlevé type |
| topic | Classical Analysis and ODEs Mathematical Physics Algebraic Geometry Complex Variables 34M35 (primary) 34M55, 33E17, 14E15 (secondary) |
| url | https://arxiv.org/abs/2402.19053 |