Jacobi Hamiltonian Integrators: construction and applications
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910003682607104 |
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| author | Araújo, Adérito Oliveira, Gonçalo Inocêncio Mestre, João Nuno |
| author_facet | Araújo, Adérito Oliveira, Gonçalo Inocêncio Mestre, João Nuno |
| contents | We propose a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds. By combining Poissonization of Jacobi structures with homogeneous symplectic bi-realizations, Jacobi dynamics are lifted to homogeneous Poisson Hamiltonian systems, enabling the construction of structure-preserving Jacobi Hamiltonian integrators. The resulting schemes are constructed explicitly and applied to a range of examples, including contact Hamiltonian systems and classical models. Numerical experiments highlight their qualitative advantages over standard integrators, including better preservation of geometric structure and improved long-time behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jacobi Hamiltonian Integrators: construction and applications Araújo, Adérito Oliveira, Gonçalo Inocêncio Mestre, João Nuno Numerical Analysis Mathematical Physics Differential Geometry Symplectic Geometry 37M15 (Primary) 37M15, 65L05, 70H05 (Secondary) We propose a systematic framework for constructing geometric integrators for Hamiltonian systems on Jacobi manifolds. By combining Poissonization of Jacobi structures with homogeneous symplectic bi-realizations, Jacobi dynamics are lifted to homogeneous Poisson Hamiltonian systems, enabling the construction of structure-preserving Jacobi Hamiltonian integrators. The resulting schemes are constructed explicitly and applied to a range of examples, including contact Hamiltonian systems and classical models. Numerical experiments highlight their qualitative advantages over standard integrators, including better preservation of geometric structure and improved long-time behavior. |
| title | Jacobi Hamiltonian Integrators: construction and applications |
| topic | Numerical Analysis Mathematical Physics Differential Geometry Symplectic Geometry 37M15 (Primary) 37M15, 65L05, 70H05 (Secondary) |
| url | https://arxiv.org/abs/2601.20799 |