Claudio Pessoa, Jorge Sotomayor
Published 2008-10-10Version 1
In this paper we study the bifurcations of a class of polycycles, called lips, occurring in generic three-parameter smooth families of vector fields on a M\"obius 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 determine, under certain genericity hypotheses, the maximum number of limits cycles that may bifurcate from a graphic belonging to the lips and we describe its bifurcation diagram.
Comments: 24 pages, 4 figures
Exponential map of germs of vector fields
Singular points in generic two-parameter families of vector fields on 2-manifold
A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
![QR code for arXiv:0810.1951 [math.DS]](http://oss.arxitics.com/images/favicon.svg)