# Polynomial differential systems with even degree have no global centers

2021

Abstract Let x ˙ = P ( x , y ) , y ˙ = Q ( x , y ) be a differential system with P and Q real polynomials, and let d = max { deg P , deg Q } . A singular point p of this differential system is a global center if R 2 ∖ { p } is filled with periodic orbits. We prove that if d is even then the polynomial differential systems have no global centers.

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