Cyclicity of nilpotent centers with minimum Andreev number
The author considers polynomial families of real planar vector fields for which the origin is a monodromic nilpotent singularity having minimum Andreev number. For such differential systems the centers are characterized by the existence of a formal inverse integrating factor. Fixed these families and under some assumptions, global bounds on the maximum number of limit cycles that can bifurcate from the center singularity under perturbations within the family are given. Although in the literature there are studies on the cyclicity of nilpotent focus, the cyclicity of centers is harder to analyze. The main reason is that Hopf bifurcation from foci is a finite-codimension bifurcation in contrast with the center bifurcation. In this work a general method for computing global upper bound on the nilpotent center cyclicity is obtained for such class of systems.
scientific article; zbMATH DE number 7137475
scientific article