Centers of planar generalized Abel equations

Abstract

We deal with the differential equationr˙=drdθ=a(θ)rn+b(θ)rm, where (r,θ) are the polar coordinates in the plane R2, m and n are integers such that m>n≥2, and a,b are C1 functions. Note that when n=2 and m=3 we have an Abel differential equation. For this class of generalized Abel equations we characterize a new family of centers.