  A topological degree based averaging principle has been proposed by J. Mawhin
in his PhD thesis [J. Mawhin, Le Probleme des Solutions Periodiques en
Mecanique non Lineaire, These de doctorat en sciences, Universite de Liege,
1969]. In his thesis the author gives analogous topological degree versions of
classical bifurcation results due to I.G. Malkin and V.K. Melnikov, namely the
conditions for bifurcation of periodic solutions from families are expressed in
term of the topological degree of the bifurcation function. Moreover, the
topological index of bifurcated periodic solutions is evaluated over that
degree. A third part of the thesis is devoted to the rate the bifurcated
periodic solutions converge when the perturbation vanishes. The
differentiability of perturbed systems is not assumed.
