New family of cubic Hamiltonian centers
type: Item
instance of: scholarly article
title: New family of cubic Hamiltonian centers
zbMATH Open document ID: 1388.34022
author: Martín Eduardo Frías-Armenta
author: Jaume Llibre
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2018-02-06T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/224220
review text: Consider the polynomial Hamiltonian system \[ \begin{aligned} {dx\over dt} &= -y-(bx+ 2cy)(x+ax^2+ bxy+ cy^2),\\ {dy\over dt} &= (1+ 2ax+ by)(x+ax^2+ bxy+ cy^2)\end{aligned}\tag{\(*\)} \] with the Hamiltonian \[ H={1\over 2} ((x+ ax^2+ bxy+ cy^2)^2+ y^2) \] under the assumption \(a^2+ b^2+ c^2\neq 0\). The authors characterize the phase portrait of \((*)\) in the Poincaré disc. They prove the existence of 11 classes of phase portraits which topologically not equivalent.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6835193
zbMATH Keywords: isochronous center
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: Poincaré disc
MaRDI profile type: Publication
OpenAlex ID: W2339353368
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DOI: 10.1007/S40590-016-0126-6
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description: scientific article; zbMATH DE number 6835193