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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.16587 |
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| _version_ | 1866914048922091520 |
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| author | Leok, M. Sardón, C. Zhao, X. |
| author_facet | Leok, M. Sardón, C. Zhao, X. |
| contents | This paper presents a unified framework for studying dynamics and integration on $q$-cosymplectic manifolds. After outlining the geometric foundations of $q$-cosymplectic structures, we derive new results concerning integrable systems and the characterization of Liouville coordinates, and further investigate the Lie integrability of $q$-evolution systems in this setting. We then develop a Hamilton--Jacobi theory tailored to multi-time Hamiltonian systems, both from an intrinsic geometric perspective and via symplectification techniques. To illustrate the applicability of the framework, we construct a $q$-cosymplectic Hamiltonian model for an extended FitzHugh-Nagumo system, providing a biologically relevant example involving three distinct temporal scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integration on $q$-Cosymplectic Manifolds Leok, M. Sardón, C. Zhao, X. Mathematical Physics This paper presents a unified framework for studying dynamics and integration on $q$-cosymplectic manifolds. After outlining the geometric foundations of $q$-cosymplectic structures, we derive new results concerning integrable systems and the characterization of Liouville coordinates, and further investigate the Lie integrability of $q$-evolution systems in this setting. We then develop a Hamilton--Jacobi theory tailored to multi-time Hamiltonian systems, both from an intrinsic geometric perspective and via symplectification techniques. To illustrate the applicability of the framework, we construct a $q$-cosymplectic Hamiltonian model for an extended FitzHugh-Nagumo system, providing a biologically relevant example involving three distinct temporal scales. |
| title | Integration on $q$-Cosymplectic Manifolds |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2509.16587 |