Nonexistence of isochronous centers in planar polynomial Hamiltonian systems of degree four

X. Jarque, J. Villadelprat

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Resum

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) y2 + D(x) y3. © 2002 Elsevier Science (USA).
Idioma originalEnglish
Pàgines (de-a)334-373
RevistaJournal of Differential Equations
Volum180
Número d'incidència2
DOIs
Estat de la publicacióPublicada - 10 d’abr. 2002

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