Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four
type: Item
instance of: scholarly article
title: Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four
zbMATH Open document ID: 1014.34020
published in: Journal of Differential Equations
publication date: 2003-07-22T00:00:00Z
review text: The authors consider centers of polynomial Hamiltonian planar differential systems \((S_H)\), \(x'=-H_y(x,y)\), \(y'=H_x(x,y)\). They prove that, if the Hamiltonian function \(H(x,y)\) is a five-degree polynomial, then the system does not have isochronous centers. This paper also contains some results for Hamiltonians of the type \(H(x,y)=A(x)+ B(x)y+C(x)y^2+ D(x)y^3\), with \(A(x)\), \(B(x)\), \(C(x)\), \(D(x)\) analytic functions. For instance, if \(D(x)=a_0 x^2+b_0 x+c_0\), \(a_0\neq 0\), then, under an additional technical assumption, the period function of any center of \((S_H)\) is unbounded.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 1750348
zbMATH Keywords: centers
zbMATH Keywords: polynomial Hamiltonian planar differential systems
author: Xavier Jarque
author: J. Villadelprat
reviewed by: Marco Sabatini
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4065
OpenAlex ID: W2027048439
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DOI: 10.1006/JDEQ.2001.4065
description: scientific article; zbMATH DE number 1750348