On novel Hamiltonian descriptions of some three-dimensional non-conservative systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912669029629952 |
|---|---|
| author | Ghosh, Aritra Ghose-Choudhury, Anindya Guha, Partha |
| author_facet | Ghosh, Aritra Ghose-Choudhury, Anindya Guha, Partha |
| contents | We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, Lü, and Qi systems. We show that all of these systems can be described in a Hamiltonian framework in which the Poisson matrix $\mathcal{J}$ is supplemented by a resistance matrix $\mathcal{R}$. While such resistive-Hamiltonian systems are manifestly non-conservative, we construct higher-degree Poisson matrices via the Jordan product as $\mathcal{N} = \mathcal{J} \mathcal{R} + \mathcal{R} \mathcal{J}$, thereby leading to new bi-Hamiltonian systems. Finally, we discuss conformal Hamiltonian dynamics on Poisson manifolds and demonstrate that by appropriately choosing the underlying parameters, the reduced three-wave-interaction model as well as the Chen and Lü systems can be described in this manner where the concomitant non-conservative part of the dynamics is described with the aid of the Euler vector field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On novel Hamiltonian descriptions of some three-dimensional non-conservative systems Ghosh, Aritra Ghose-Choudhury, Anindya Guha, Partha Mathematical Physics Dynamical Systems Symplectic Geometry Chaotic Dynamics Exactly Solvable and Integrable Systems We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, Lü, and Qi systems. We show that all of these systems can be described in a Hamiltonian framework in which the Poisson matrix $\mathcal{J}$ is supplemented by a resistance matrix $\mathcal{R}$. While such resistive-Hamiltonian systems are manifestly non-conservative, we construct higher-degree Poisson matrices via the Jordan product as $\mathcal{N} = \mathcal{J} \mathcal{R} + \mathcal{R} \mathcal{J}$, thereby leading to new bi-Hamiltonian systems. Finally, we discuss conformal Hamiltonian dynamics on Poisson manifolds and demonstrate that by appropriately choosing the underlying parameters, the reduced three-wave-interaction model as well as the Chen and Lü systems can be described in this manner where the concomitant non-conservative part of the dynamics is described with the aid of the Euler vector field. |
| title | On novel Hamiltonian descriptions of some three-dimensional non-conservative systems |
| topic | Mathematical Physics Dynamical Systems Symplectic Geometry Chaotic Dynamics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.10729 |