18 research outputs found
On the separatrix graph of a rational vector field on the Riemann sphere
We consider the rational flow where is given by
the quotient of two polynomials without common factors on the Riemann sphere.
The separatrix graph 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.Comment: 25 pages, 14 figure
Classification of Complex Polynomial Vector Fields in One Complex Variable
A classification of the global structure of monic and centered one-variable
complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference
Equations and Application