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arXiv · 2605.26342

Rotation number for a homogeneous vector field in $\mathbf{C}^{2}$

Adrien Kachkachi
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Abstract

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.

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Adrien Kachkachi. 2026-05-25. Rotation number for a homogeneous vector field in $\mathbf{C}^{2}$. https://arxiv.org/abs/2605.26342

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