Abstract:

In this talk we study the bifurcations of a class of polycycles, called lips, occurring in generic three-parameter smooth families of vector fields on a Möbius band. The lips consists of a set of polycycles formed by two saddle-nodes, one attracting and the other repelling, connected by the hyperbolic separatrices of the saddle-nodes and by orbits interior to both nodal sectors. We describe its bifurcation diagram and also talk about the possible formulations of this problem for three dimensional.