Cyclicity of Nilpotent Centers with Minimum Andreev Number

Abstract

We consider polynomial families of real planar vector fields for which the origin is a monodromic nilpotent singularity having minimum Andree's number. There the centers are characterized by the existence of a formal inverse integrating factor. For such families we give, under some assumptions, global bounds on the maximum number of limit cycles that can bifurcate from the singularity under perturbations within the family.

The author is partially supported by the MINECO Grant Number MTM2017-84383-P and the AGAUR Grant Number 2017SGR-1276.