Bifurcations in a class of polycycles involving two saddle-nodes on a Mobius band

Details Bifurcations in a class of polycycles involving two saddle-nodes on a Mobius band Bifurcations in a class of polycycles involving two saddle-nodes on a Mobius band

2008-10-10

arxiv.org/abs/0810.1951v1

Mathematics

Dynamical Systems

24 pages, 4 figures

Scientific paper

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.

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