ABSTRACT
Introduction This is a continuation of Chapter 7 because we are again considering the existence of periodic solutions in a perturbation problem and the underlying approach is again the Poincare´ method. But now the unperturbed and perturbed equations are both autonomous. That is, we consider an equation of the form
dx dt
= f (x, ε)
Following a common usage, we term such problems bifurcation problems. The fact that the unperturbed and perturbed equations are both autonomous
introduces two complications: First, we have few hints about the period of any such desired periodic solution; second, as observed before, if x(t) is a solution of period T of an autonomous equation then x(t + k), where k is an arbitrary real number, is also a solution of period T . Thus the unperturbed equation has either no periodic solution or a continuous family of periodic solutions.
