Bifurcations in a class of polycycles involving two saddle-nodes on a Mobius band
Dynamical Systems
2008-10-14 v1
Abstract
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.
Cite
@article{arxiv.0810.1951,
title = {Bifurcations in a class of polycycles involving two saddle-nodes on a Mobius band},
author = {Claudio Pessoa and Jorge Sotomayor},
journal= {arXiv preprint arXiv:0810.1951},
year = {2008}
}
Comments
24 pages, 4 figures