Some stability properties of Hamiltonian Poisson integrators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911273953787904 |
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| author | Cosserat, Oscar |
| author_facet | Cosserat, Oscar |
| contents | Hamiltonian Poisson integrators are Poisson integrators that admit a modified Hamiltonian. In this article, we illustrate the importance of the existence of a modified Hamiltonian for Poisson integrators in the context of integrable and non-integrable systems. Examples of Hamiltonian systems are provided by Lotka-Volterra dynamics; in order to investigate stability properties of Hamiltonian Poisson integrators on non-integrable systems, we exhibit a non-integrable $5$-dimensional Lotka-Volterra system and pursue numerical investigations of it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some stability properties of Hamiltonian Poisson integrators Cosserat, Oscar Numerical Analysis Mathematical Physics Differential Geometry Dynamical Systems Symplectic Geometry Hamiltonian Poisson integrators are Poisson integrators that admit a modified Hamiltonian. In this article, we illustrate the importance of the existence of a modified Hamiltonian for Poisson integrators in the context of integrable and non-integrable systems. Examples of Hamiltonian systems are provided by Lotka-Volterra dynamics; in order to investigate stability properties of Hamiltonian Poisson integrators on non-integrable systems, we exhibit a non-integrable $5$-dimensional Lotka-Volterra system and pursue numerical investigations of it. |
| title | Some stability properties of Hamiltonian Poisson integrators |
| topic | Numerical Analysis Mathematical Physics Differential Geometry Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2511.14303 |