Formal Paths, Iterated Integrals and the Center Problem for Ordinary Differential Equations

Abstract

We continue the study of the center problem for the ordinary differential equation $v^{\prime }={\sum }_{i=1}^{\infty }{a}_i(x)v^{i+1}$ started in our earlier papers. In this paper we present the highlights of the algebraic theory of centers.

35 pages