Solvability of planar complex vector fields with homogeneous singularities

Abstract

In this paper, we study the equation , where L is a -valued vector field in with a homogeneous singularity. The properties of the solutions are linked to the number theoretic properties of a pair of complex numbers attached to the vector field. As an application, we obtain results about an associated Riemann–Hilbert problem for the vector field L.

Keywords:

• Vector field
• homogeneous
• first integral
• Riemann-Hilbert problem

AMS Subject Classifications:

• Primary: 35A01
• 35F05
• Secondary: 35F15

Notes

No potential conflict of interest was reported by the author.