Rotation number for a homogeneous vector field in $\mathbf{C}^{2}$
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913168033316864 |
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| author | Kachkachi, Adrien |
| author_facet | Kachkachi, Adrien |
| contents | In this paper, we use affine surfaces to describe completely the real-time trajectories of a homogeneous vector field in $\mathbf{C}^{2}$. We prove the existence of a continuous "rotation number" in $\mathbf{C}^{2}$ which is constant along real-time trajectories. A description of the trajectories depending on their rotation number is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26342 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rotation number for a homogeneous vector field in $\mathbf{C}^{2}$ Kachkachi, Adrien Dynamical Systems In this paper, we use affine surfaces to describe completely the real-time trajectories of a homogeneous vector field in $\mathbf{C}^{2}$. We prove the existence of a continuous "rotation number" in $\mathbf{C}^{2}$ which is constant along real-time trajectories. A description of the trajectories depending on their rotation number is given. |
| title | Rotation number for a homogeneous vector field in $\mathbf{C}^{2}$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.26342 |