Some New Results on Abel Equations

Abel equations of the form r aŽt.r2 bŽt.r3, t t0, t1 , are of interest because of their close relation to planar vector fields. In this paper three new results on Abel equations are presented: Ž1. An asymptotic expansion of the solutions of Abel equations in terms of the coefficient functions aŽ . and bŽ .. Ž2.A simple recurrence relation for Bautin quantities of Abel equations. Ž3. A center condition for a class of polynomial Abel equations.