Abstract:

Recall that the Balance Harmonic method provides a heuristic method for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. In this talk we recover the pioneering results of Stokes and Urabe that provide a theoretical basis for proving that near this truncated series there is an actual periodic orbit of the equation. We will restrict our attention to one-dimensional autonomous ordinary differential equations and we apply the results obtained to a couple of concrete examples coming from planar autonomous systems.

This talk is based on a joint work with Johanna D. García.