Alexander Brudnyi , Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4; e-mail: albru@math.ucalgary.ca

Abstract/Résumé:

We present a solution of the problem of characterization of the universal centers of a differential equation $v’=\sum_{j=1}^n a_j v^{j+1}$ with all $a_j$ real analytic in a neighbourhood of $[a,b]\Subset\mathbb{R}$ in terms of the vanishing of finitely many moments determined by $a_1, \ldots, a_n$.

On présente la solution du problème de caractériser les centres universels d’une équation différentielle $v’=\sum_{j=1}^n a_j v^{j+1}$ dont tous les coefficients sont des fonctions analytiques réelles autour de $[a,b]\Subset\mathbb{R}$ en utilisant les ensembles des zéros d’un nombre fini des moments calculés en partant des fonctions $a_1, \ldots, a_n$

Keywords: Lipschitz curve, Moment, center problem, homology, polynomial approximation, unicursal curve

AMS Subject Classification: Moment problems 44A60

PDF(click to download): On Characterization of Universal Centers of ODEs with Analytic Coefficients