Polynomial differential systems with hyperbolic algebraic limit cycles

Abstract

For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations. These systems admit precisely the bounded components of the curve as limit cycles.

Keywords

• sixteenth problem of hilbert
• planar differential system
• invariant curve
• periodic solution
• hyperbolic limit cycle