$k$-contact Lie systems: theory and applications
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915632448012288 |
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| author | de Lucas, Javier Rivas, Xavier Sobczak, Tomasz |
| author_facet | de Lucas, Javier Rivas, Xavier Sobczak, Tomasz |
| contents | This paper introduces a new class of Lie systems that are Hamiltonian relative to a $k$-contact manifold. We show that a recent distributional approach to $k$-contact manifolds along with a related $k$-contact Hamiltonian vector field notion allow us to understand relevant Lie systems as Hamiltonian relative to a $k$-contact manifold. Our procedure is more general than previously known methods with this aim. As a result, we find that a plethora of Lie systems related to control and physical problems can be considered in a natural manner as $k$-contact Lie systems. We study their $t$-dependent and $t$-independent constants of motion, master symmetries of higher order, and other properties of interest. Finally, we use our new techniques and findings to study PDE Lie systems with a compatible $k$-contact manifold, some of which become Hamilton--De Donder--Weyl equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $k$-contact Lie systems: theory and applications de Lucas, Javier Rivas, Xavier Sobczak, Tomasz Differential Geometry This paper introduces a new class of Lie systems that are Hamiltonian relative to a $k$-contact manifold. We show that a recent distributional approach to $k$-contact manifolds along with a related $k$-contact Hamiltonian vector field notion allow us to understand relevant Lie systems as Hamiltonian relative to a $k$-contact manifold. Our procedure is more general than previously known methods with this aim. As a result, we find that a plethora of Lie systems related to control and physical problems can be considered in a natural manner as $k$-contact Lie systems. We study their $t$-dependent and $t$-independent constants of motion, master symmetries of higher order, and other properties of interest. Finally, we use our new techniques and findings to study PDE Lie systems with a compatible $k$-contact manifold, some of which become Hamilton--De Donder--Weyl equations. |
| title | $k$-contact Lie systems: theory and applications |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.17734 |