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Cyclicity of nilpotent centers with minimum Andreev number

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Abstract

We consider polynomial families of real planar vector fields for which the origin is a monodromic nilpotent singularity having minimum Andreev 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.

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Authors and Affiliations

  1. Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001, Lleida, Spain

    Isaac A. García

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  1. Isaac A. García
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Correspondence to Isaac A. García.

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

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García, I.A. Cyclicity of nilpotent centers with minimum Andreev number. European Journal of Mathematics 5, 1293–1330 (2019). https://doi.org/10.1007/s40879-018-0304-3

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