On analytic insolubility of the stability problem on the plane

Abstract

This is a survey on questions involving algebraic and analytic solubility of the problem of stability of a singular point of a vector field on the plane, and in particular of the problem of distinguishing between a centre and a focus. It is proved that the stability problem on the plane is analytically insoluble. © 2013 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.