Asymptotic stability of forced oscillations

The study of forced oscillations emanating from a limit cycle is a classical problem in the theory of bifurcation. Around 1950 the basic method to deal with this problem was developed by Malkin in [11] and this study was continued by Loud in [10]. The state of the art before the contributions of Malkin and Loud can be found in the book by Lefschetz [9]. To describe the general framework we start with a