Abstract

The knowledge of a family of planar vector fields X_lambda is principally linked to the knowledge of the bifurcations which occur in the neigbourhood of its limit periodic sets (possible limit of sequences of limit cycles). Bifurcations of limit cycles near a limit periodic set Gamma are bifurcations of isolated fixed points of the family of return maps P_lambda(h) associated to Gamma. They depend essentially of the asymptotic properties of P_lambda(h). In this talk I want to review the different possible asymptotics to compare them and to recall the tools what are used in their study. It will give me the opportunuty to list several open questions which can be asked about each type of asymptotics, even for the more simpler ones.