On the global stability of the Lorentz system (Q1071928)

The author extends a method of iterated averages for investigating stability questions for ordinary differential equations. The main goal is to show that the existence and stability of quasi-periodic solutions is determined by the existence and conditional stability of a rest point of the associated iterated average system. An example is given of the use of the method to obtain the existence of a quasi-periodic solution in the presence of a Hopf bifurcation.