Проблема центра и фокуса для одной кубической системы в случае нулевых собственных значений линейной части

Abstract

The center and focus problem has been solved for systems x =y+P 2 (x, y)+Pз(дг, у), у where P„ i=2, 3, - homogeneous polynomial of degree There is proven the existence of such systems with six limit cycles in a neighbourhood of the point 0(0, 0).