2008/10/10 by Claudio Pessoa, Pessoa, Claudio, Jorge Sotomayor +1
Computer Science · Mathematics · Physics and Astronomy · #34C35 #34D30 #58F09 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS #msc:34C35 #msc:34D30 #msc:58F09
paper · pdf · doi:10.48550/arxiv.0810.1951
24 pages, 4 figures
arxiv created 2008/10/10 · openalex publication_date 2008/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 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.