Cyclicity of nilpotent centers with minimum Andreev number
type: Item
instance of: scholarly article
title: Cyclicity of nilpotent centers with minimum Andreev number
zbMATH Open document ID: 1458.34062
published in: European Journal of Mathematics
publication date: 2019-11-27T00:00:00Z
full work available at URL: http://hdl.handle.net/10459.1/67895
review text: 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.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 7137475
zbMATH Keywords: monodromic singularity
zbMATH Keywords: nilpotent center
zbMATH Keywords: cyclicity
zbMATH Keywords: inverse integrating factor
author: Isaac A. García
reviewed by: Jaume Giné
describes a project that uses: SINGULAR
describes a project that uses: primdec
MaRDI profile type: Publication
OpenAlex ID: W2900637666
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Wikidata QID: Q128990578
DOI: 10.1007/S40879-018-0304-3
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description: scientific article; zbMATH DE number 7137475