Estimation of a position of the periodic solution of autonomous systems
"Математика. Компьютер. Образование". Cб. трудов X международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2003. Vol. 2. Pp. 95-102.
The problem of existence of the periodic solutions for autonomous systems of the ordinary differential equations with a null matrix of linear approximation is considered. It is supposed, that the right part of a system is the sum of the forms of coordinates of vectors of the solution and parameter. The necessary and sufficient conditions of existence of the periodic solution in a vicinity of origin of coordinates are formulated. The method to estimate a position of the periodic solution in the vicinity of zero to with precision to a sector is presented. The similar problem were also put in work  for nonautonomous systems. In work  the way of definition of the period for autonomous systems is given.