Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
type: Item
instance of: scholarly article
title: Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
zbMATH Open document ID: 1369.34057
author: Ilker E. Colak
author: Jaume Llibre
author: Claudia Valls
published in: Journal of Differential Equations
publication date: 2017-03-16T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/182488
review text: In [Adv. Math. 259, 655--687 (2014; Zbl 1303.34027)], the authors provided the normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields. In [J. Math. Anal. Appl. 433, No. 1, 305--319 (2016; Zbl 1336.34047)], \textit{M. Dukarić} et al. provided the global phase portraits in the Poincaré disk for all reversible nilpotent centers with cubic homogeneous nonlinearities planar polynomial vector fields. These two works complete the classification of the phase portraits of the nilpotent centers with cubic homogeneous nonlinearities. In the present work, the authors give the bifurcation diagrams for the global phase portraits in the Poincaré disk of the first planar polynomial vector fields.
reviewed by: Jaume Giné
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C08
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 6695505
zbMATH Keywords: Hamiltonian nilpotent center
zbMATH Keywords: cubic polynomial
zbMATH Keywords: vector fields
zbMATH Keywords: phase portrait
zbMATH Keywords: bifurcation diagram
MaRDI profile type: Publication
OpenAlex ID: W4205459963
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DOI: 10.1016/J.JDE.2017.02.001
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description: scientific article; zbMATH DE number 6695505