Kahan-Hirota-Kimura maps preserving original cubic hamiltonians
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908388213915648 |
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| author | Mañosa, Víctor Pantazi, Chara |
| author_facet | Mañosa, Víctor Pantazi, Chara |
| contents | We study the class of cubic Hamiltonian vector fields whose associated Kahan-Hirota-Kimura (KHK) maps preserve the original Hamiltonian function. Our analysis focuses on these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$, extending to a family of fields in $\mathbb{R}^6$. Additionally, we investigate various properties of these fields, including the existence of additional first integrals of a specific type, their role as Lie symmetries of the corresponding KHK map, and the symplecticity of these maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kahan-Hirota-Kimura maps preserving original cubic hamiltonians Mañosa, Víctor Pantazi, Chara Exactly Solvable and Integrable Systems Dynamical Systems 37J35, 37J11, 37J70, 37M15, 14E05 We study the class of cubic Hamiltonian vector fields whose associated Kahan-Hirota-Kimura (KHK) maps preserve the original Hamiltonian function. Our analysis focuses on these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$, extending to a family of fields in $\mathbb{R}^6$. Additionally, we investigate various properties of these fields, including the existence of additional first integrals of a specific type, their role as Lie symmetries of the corresponding KHK map, and the symplecticity of these maps. |
| title | Kahan-Hirota-Kimura maps preserving original cubic hamiltonians |
| topic | Exactly Solvable and Integrable Systems Dynamical Systems 37J35, 37J11, 37J70, 37M15, 14E05 |
| url | https://arxiv.org/abs/2405.01321 |