On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems
type: Item
instance of: scholarly article
title: On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems
zbMATH Open document ID: 1453.37054
author: Jaume Llibre
author: Dongmei Xiao
published in: Pacific Journal of Mathematics
publication date: 2020-08-10T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/232598
review text: This paper proposes a study of centers and their configurations for Hamiltonian cubic polynomial differential systems having two intersecting invariant straight lines. By applying an affine transformation these two invariant straight lines go through the axes of coordinates and these systems become Kolmogorov systems. The authors find that the real algebraic curve \(xy(a+bx+cy+dx^2+exy+fy^2)=h\) has at most four families of level ovals in the phase plane of such systems for all real parameters \(a\), \(b\), \(c\), \(d\), \(e\), \(f\) and \(h\).
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 7229711
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Kolmogorov systems
zbMATH Keywords: cubic polynomial differential systems
zbMATH Keywords: centers
zbMATH Keywords: configuration of centers
MaRDI profile type: Publication
OpenAlex ID: W3043767843
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DOI: 10.2140/PJM.2020.306.611
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description: scientific article; zbMATH DE number 7229711