Moments Finiteness Problem and Center Problem for Ordinary Differential Equations

TL;DR

This paper investigates the moments finiteness problem for Lipschitz maps into Lipschitz triangulable curves and applies the results to identify universal centers in certain ODEs through finitely many moments.

Contribution

It introduces new results on the moments finiteness problem and applies them to the center problem for ODEs with analytic coefficients.

Findings

Characterization of moments finiteness for Lipschitz maps into triangulable curves

Application to the center problem in differential equations

Identification of universal centers via finitely many moments

Abstract

We study the moments finiteness problem for the class of Lipschitz maps $F: [a,b]\rightarrow\mathbb R^n$ with images in a compact Lipschitz triangulable curve $\Gamma$. We apply the obtained results to the center problem for ODEs describing in some cases (including equations with analytic coefficients) the set of universal centers of such equations by vanishing of finitely many moments from their coefficients.