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Nonexistence of Isochronous Centers in Planar Polynomial Hamiltonian Systems of Degree Four

Authors
Journal
Journal of Differential Equations
0022-0396
Publisher
Elsevier
Publication Date
Volume
180
Issue
2
Identifiers
DOI: 10.1006/jdeq.2001.4065
Disciplines
  • Mathematics

Abstract

Abstract In this paper we study centers of planar polynomial Hamiltonian systems and we are interested in the isochronous ones. We prove that every center of a polynomial Hamiltonian system of degree four (that is, with its homogeneous part of degree four not identically zero) is nonisochronous. The proof uses the geometric properties of the period annulus and it requires the study of the Hamiltonian systems associated to a Hamiltonian function of the form H( x, y)= A( x)+ B( x) y+ C( x) y 2+ D( x) y 3.

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