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

Identificador:  imarina:9162283

Handle: https://hdl.handle.net/20.500.11797/imarina9162283

Autors:  Dias, Kealey; Garijo, Antonio

Resum:
© 2021 Elsevier Inc. We consider the rational flow ξR(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 ΓR is the boundary between trajectories with different properties. We characterize the properties of a planar directed graph to be the separatrix graph of a rational vector field on the Riemann sphere.