The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities

Abstract

We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$. We study the algebraic and non-algebraic invariant curves of these systems with emphasis on limit cycles.

Keywords

• polynomial systems
• algebraic limit cycles