Abstract

The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e., the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to it. In this work we provide sufficient conditions in order that the averaging theory can be applied also to non-simple zeros for studying their associated periodic solutions. Additionally, we Apply this result for studying the zero-Hopf bifurcation in the Lorenz system.