Multisymplectic structure of nonintegrable Henon-Heiles system
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913681287151616 |
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| author | Tsiganov, A. V. |
| author_facet | Tsiganov, A. V. |
| contents | Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent symplectic structure. In this note, the second invariant symplectic form is presented for the nonintegrable Henon-Heiles system, Kepler problem, integrable and non-integrable Toda type systems. This approach facilitates the construction of a multi-symplectic integrator, which effectively preserves both symplectic forms for these benchmark problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multisymplectic structure of nonintegrable Henon-Heiles system Tsiganov, A. V. Dynamical Systems Mathematical Physics Exactly Solvable and Integrable Systems Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent symplectic structure. In this note, the second invariant symplectic form is presented for the nonintegrable Henon-Heiles system, Kepler problem, integrable and non-integrable Toda type systems. This approach facilitates the construction of a multi-symplectic integrator, which effectively preserves both symplectic forms for these benchmark problems. |
| title | Multisymplectic structure of nonintegrable Henon-Heiles system |
| topic | Dynamical Systems Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2502.03786 |