Method for Constructing Periodic Solutions of Nonlinear Differential Equations.

We justify an analytical method for constructing periodic solutions of nonlinear systems of ordinary differential equations of polynomial type. Periodic solutions are constructed in the form of Fourier series in which the coefficients are polynomials depending on a parameter, which is not assumed to be small. Two examples are considered: the van der Pol equation and the Lorenz system. [ABSTRACT FROM AUTHOR]