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arXiv · 2010.00066

On the separatrix graph of a rational vector field on the Riemann sphere

Kealey Dias·Antonio Garijo
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Abstract

We consider the rational flow $\xi_R(z)= R(z) (d/dz)$ where $R$ is given by the quotient of two polynomials without common factors on the Riemann sphere. The separatrix graph $\Gamma_R$ is the boundary between trajectories with different properties. We characterize the properties of a planar directed graph to be homeomorphic to the separatrix graph of a rational vector field on the Riemann sphere.

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Kealey Dias, Antonio Garijo. 2020-09-30. On the separatrix graph of a rational vector field on the Riemann sphere. https://arxiv.org/abs/2010.00066

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